Decimals

Convert the following decimals into like decimals :

8.1, 9.4, 6.05, 12

Answer

Given:

8.1, 9.4, 6.05, 12

To convert into like decimals, we make the number of decimal places equal.

The maximum number of decimal places is 2 (in 6.05).

So,

8.1 = 8.10
9.4 = 9.40
6.05 = 6.05
12 = 12.00

∴ Like decimals are 8.10, 9.40, 6.05 and 12.00

Convert the following decimals into like decimals :

6.35, 11.8, 9.125, 32.04, 9

Answer

Given:

6.35, 11.8, 9.125, 32.04, 9

The maximum number of decimal places is 3 (in 9.125).

So,

6.35 = 6.350
11.8 = 11.800
9.125 = 9.125
32.04 = 32.040
9 = 9.000

∴ Like decimals are 6.350, 11.800, 9.125, 32.040 and 9.000

Convert the following decimals into like decimals :

6.005, 2, 0.6, 1.78, 14.3

Answer

Given:

6.005, 2, 0.6, 1.78, 14.3

The maximum number of decimal places is 3 (in 6.005).

So,

6.005 = 6.005
2 = 2.000
0.6 = 0.600
1.78 = 1.780
14.3 = 14.300

∴ Like decimals are 6.005, 2.000, 0.600, 1.780 and 14.300

Convert the following decimals into like decimals :

0.72, 53.76, 16, 8.304, 2.3754

Answer

Given:

0.72, 53.76, 16, 8.304, 2.3754

Maximum decimal places = 4

So,

0.72 = 0.7200
53.76 = 53.7600
16 = 16.0000
8.304 = 8.3040
2.3754 = 2.3754

∴ Like decimals are 0.7200, 53.7600, 16.0000, 8.3040 and 2.3754

Write each of the following decimals into expanded form :

16.74

Answer

We have:

16.74 = 10 + 6 + 0.7 + 0.04 $\hspace{2cm}$[Separating according to place values]

$= (1 \times 10) + (6 \times 1) + \Big(7 \times \dfrac{1}{10}\Big) + \Big(4 \times\dfrac{1}{100}\Big) \\[1em] = 10 + 6 + \dfrac{7}{10} + \dfrac{4}{100}$

∴ The expanded form of 16.74 is $\Big(10 + 6 + \dfrac{7}{10} + \dfrac{4}{100}\Big)$

Write each of the following decimals into expanded form :

243.689

Answer

We have:

243.689 = 200 + 40 + 3 + 0.6 + 0.08 + 0.009 [Separating according to place values]

$= (2 \times 100) + (4 \times 10) + (3 \times 1) + \Big(6 \times \dfrac{1}{10}\Big) + \Big(8 \times \dfrac{1}{100}\Big) + \Big(9 \times \dfrac{1}{1000}\Big) \\[1em] = 200 + 40 + 3 + \dfrac{6}{10} + \dfrac{8}{100} + \dfrac{9}{1000}$

∴ The expanded form of 243.689 is $\Big(200 + 40 + 3 + \dfrac{6}{10} + \dfrac{8}{100} + \dfrac{9}{1000}\Big)$

Write each of the following decimals into expanded form :

9.3578

Answer

We have:

9.3578 = 9 + 0.3 + 0.05 + 0.007 + 0.0008 [Separating according to place values]

$= (9 \times 1) + \Big(3 \times \dfrac{1}{10}\Big) + \Big(5 \times \dfrac{1}{100}\Big) + \Big(7 \times \dfrac{1}{1000}\Big) + \Big(8 \times \dfrac{1}{10000}\Big) \\[1em] = 9 + \dfrac{3}{10} + \dfrac{5}{100} + \dfrac{7}{1000} + \dfrac{8}{10000}$

∴ The expanded form of 9.3578 is $\Big(9 + \dfrac{3}{10} + \dfrac{5}{100} + \dfrac{7}{1000} + \dfrac{8}{10000}\Big)$

Write each of the following decimals into expanded form :

2314.57

Answer

We have:

2314.57 = 2000 + 300 + 10 + 4 + 0.5 + 0.07 [Separating according to place values]

$= (2 \times 1000) + (3 \times 100) + (1 \times 10) + (4 \times 1) + \Big(5 \times \dfrac{1}{10}\Big) + \Big(7 \times \dfrac{1}{100}\Big) \\[1em] = 2000 + 300 + 10 + 4 + \dfrac{5}{10} + \dfrac{7}{100}$

∴ The expanded form of 2314.57 is $\Big(2000 + 300 + 10 + 4 + \dfrac{5}{10} + \dfrac{7}{100}\Big)$

Express the following as a fraction in simplest form :

0.8

Answer

We have:

0.8

There is 1 decimal place, so we remove the decimal point and divide by 10.

$\phantom{=} 0.8 = \dfrac{8}{10} \\[1em] = \dfrac{4}{5} \quad \text{[Dividing both by 2]}$

∴ The answer is $\dfrac{4}{5}$

Express the following as a fraction in simplest form :

0.45

Answer

We have:

0.45

There are 2 decimal places, so we remove the decimal point and divide by 100.

$\phantom{=} 0.45 = \dfrac{45}{100} \\[1em] = \dfrac{9}{20} \quad \text{[Dividing both by 5]}$

∴ The answer is $\dfrac{9}{20}$

Express the following as a fraction in simplest form :

1.6

Answer

We have:

1.6

There is 1 decimal place, so we remove the decimal point and divide by 10.

$\phantom{=} 1.6 = \dfrac{16}{10} \\[1em] = \dfrac{8}{5} \quad \text{[Dividing both by 2]} \\[1em] = 1\dfrac{3}{5}$

∴ The answer is $1\dfrac{3}{5}$

Express the following as a fraction in simplest form :

4.75

Answer

We have:

4.75

There are 2 decimal places, so we remove the decimal point and divide by 100.

$\phantom{=} 4.75 = \dfrac{475}{100} \\[1em] = \dfrac{19}{4} \quad \text{[Dividing both by 25]} \\[1em] = 4\dfrac{3}{4}$

∴ The answer is $4\dfrac{3}{4}$

Express the following as a fraction in simplest form :

0.345

Answer

We have:

0.345

There are 3 decimal places, so we remove the decimal point and divide by 1000.

$\phantom{=} 0.345 = \dfrac{345}{1000} \\[1em] = \dfrac{69}{200} \quad \text{[Dividing both by 5]}$

∴ The answer is $\dfrac{69}{200}$

Express the following as a fraction in simplest form :

64.015

Answer

We have:

64.015

There are 3 decimal places, so we remove the decimal point and divide by 1000.

$\phantom{=} 64.015 = \dfrac{64015}{1000} \\[1em] = \dfrac{12803}{200} \quad \text{[Dividing both by 5]} \\[1em] = 64\dfrac{3}{200}$

∴ The answer is $64\dfrac{3}{200}$

Express the following as a fraction in simplest form :

12.725

Answer

We have:

12.725

There are 3 decimal places, so we remove the decimal point and divide by 1000.

$\phantom{=} 12.725 = \dfrac{12725}{1000} \\[1em] = \dfrac{509}{40} \quad \text{[Dividing both by 25]} \\[1em] = 12\dfrac{29}{40}$

∴ The answer is $12\dfrac{29}{40}$

Express the following as a fraction in simplest form :

0.0024

Answer

We have:

0.0024

There are 4 decimal places, so we remove the decimal point and divide by 10000.

$\phantom{=} 0.0024 = \dfrac{24}{10000} \\[1em] = \dfrac{3}{1250} \quad \text{[Dividing both by 8]}$

∴ The answer is $\dfrac{3}{1250}$

Convert the following fraction into a decimal :

$\dfrac{19}{10}$

Answer

We have:

$\phantom{=} \dfrac{19}{10} = 1\dfrac{9}{10} \quad \text{[Converting improper to mixed fraction]} \\[1em] = 1 + \dfrac{9}{10} \\[1em] = 1 + 0.9 \\[1em] = 1.9$

∴ The answer is 1.9

Convert the following fraction into a decimal :

$\dfrac{243}{100}$

Answer

We have:

$\phantom{=} \dfrac{243}{100} = 2\dfrac{43}{100} \quad \text{[Converting improper to mixed fraction]} \\[1em] = 2 + \dfrac{43}{100} \\[1em] = 2 + 0.43 \\[1em] = 2.43$

∴ The answer is 2.43

Convert the following fraction into a decimal :

$\dfrac{51}{100}$

Answer

We have:

$\dfrac{51}{100} = 0.51$

∴ The answer is 0.51

Convert the following fraction into a decimal :

$\dfrac{9}{100}$

Answer

We have:

$\dfrac{9}{100} = 0.09$

∴ The answer is 0.09

Convert the following fraction into a decimal :

$\dfrac{72}{1000}$

Answer

We have:

$\dfrac{72}{1000} = 0.072$

∴ The answer is 0.072

Convert the following fraction into a decimal :

$\dfrac{3}{5}$

Answer

We have:

$\phantom{=} \dfrac{3}{5} = \dfrac{3 \times 2}{5 \times 2} \quad \text{[Multiplying by 2 to get denominator 10]} \\[1em] = \dfrac{6}{10} \\[1em] = 0.6$

∴ The answer is 0.6

Convert the following fraction into a decimal :

$\dfrac{7}{8}$

Answer

We have:

$\phantom{=} \dfrac{7}{8} = \dfrac{7 \times 125}{8 \times 125} \quad \text{[Multiplying by 125 to get denominator 1000]} \\[1em] = \dfrac{875}{1000} \\[1em] = 0.875$

∴ The answer is 0.875

Convert the following fraction into a decimal :

$\dfrac{37}{40}$

Answer

We have:

$\phantom{=} \dfrac{37}{40} = \dfrac{37 \times 25}{40 \times 25} \hspace{2cm}\text{[Multiplying by 25 to get denominator 1000]} \\[1em] = \dfrac{925}{1000} \\[1em] = 0.925$

∴ The answer is 0.925

Convert the following fraction into a decimal :

$4\dfrac{3}{8}$

Answer

First, we convert the mixed fraction into an improper fraction:

$\phantom{=} 4\dfrac{3}{8} = \dfrac{4 \times 8 + 3}{8} = \dfrac{32 + 3}{8} = \dfrac{35}{8}$

Now, we divide 35 by 8. Since 35 is not exactly divisible by 8, we add a decimal point and zeros to continue the division:

$\begin{array}{r} 4.375 \\ 8 \overline{) 35.000} \\ \underline{-32\phantom{.000}} \\ 30\phantom{00} \\ \underline{-24\phantom{00}} \\ 60\phantom{0} \\ \underline{-56\phantom{0}} \\ 40 \\ \underline{-40} \\ 0 \end{array}$

$\dfrac{35}{8}$ = 4.375

∴ $4\dfrac{3}{8}$ = 4.375

Convert the following fraction into a decimal :

$9\dfrac{1}{25}$

Answer

First, we convert the mixed fraction into an improper fraction:

$\phantom{=} 9\dfrac{1}{25} = \dfrac{9 \times 25 + 1}{25} = \dfrac{225 + 1}{25} = \dfrac{226}{25}$

Now, we divide 226 by 25. Since 226 is not exactly divisible by 25, we add a decimal point and zeros to continue the division:

$\begin{array}{r} 9.04 \\ 25 \overline{) 226.00} \\ \underline{-225\phantom{00}} \\ 100 \\ \underline{-100} \\ 0 \end{array}$

$\dfrac{226}{25}$ = 9.04

∴ $9\dfrac{1}{25}$ = 9.04

Convert the following fractions into a decimal :

$2\dfrac{9}{16}$

Answer

First, we convert the mixed fraction into an improper fraction:

$\phantom{=} 2\dfrac{9}{16} = \dfrac{2 \times 16 + 9}{16} = \dfrac{32 + 9}{16} = \dfrac{41}{16}$

Now, we divide 41 by 16. We add a decimal point and zeros to continue the division:

$\begin{array}{r} 2.5625 \\ 16 \overline{) 41.0000} \\ \underline{-32\phantom{.0000}} \\ 90\phantom{000} \\ \underline{-80\phantom{000}} \\ 100\phantom{00} \\ \underline{-096\phantom{00}} \\ 40\phantom{0} \\ \underline{-32\phantom{0}} \\ 80 \\ \underline{-80} \\ 0 \end{array}$

$\dfrac{41}{16}$ = 2.5625

∴ $2\dfrac{9}{16}$ = 2.5625

Convert the following fractions into a decimal :

$4\dfrac{11}{125}$

Answer

First, we convert the mixed fraction into an improper fraction:

$4\dfrac{11}{125} = \dfrac{4 \times 125 + 11}{125} = \dfrac{500 + 11}{125} = \dfrac{511}{125}$

Now, we divide 511 by 125. We add a decimal point and zeros to continue the division:

$\begin{array}{r} 4.088 \\ 125 \overline{) 511.000} \\ \underline{-500\phantom{.000}} \\ 1100\phantom{0} \\ \underline{-1000\phantom{0}} \\ 1000 \\ \underline{-1000} \\ 0 \end{array}$

$\dfrac{511}{125}$ = 4.088

∴ $4\dfrac{11}{125}$ = 4.088

Add:

9.67, 15.98

Answer

The maximum number of decimal places is 2. The numbers are already like decimals.

On adding column-wise, we get:

$\begin{array}{r} 9.67 \\ +\phantom{0}15.98 \\ \hline 25.65 \\ \hline \end{array}$

Hence, the sum is 25.65

Add:

6.9, 23.84

Answer

Maximum number of decimal places in given decimals is 2. So, we convert them into like decimals, each having 2 places of decimal, by annexing zeros.

$\begin{array}{r} 6.90 \\ +\phantom{0}23.84 \\ \hline 30.74 \\ \hline \end{array}$

Hence, the sum is 30.74

Add:

35.67, 18.794, 4.9, 31.82

Answer

Maximum number of decimal places in given decimals is 3. So, we convert them into like decimals, each having 3 places of decimal, by annexing zeros.

Thus, we get: 35.670, 18.794, 4.900 and 31.820

On adding column-wise, we get:

$\begin{array}{r} 35.670 \\ 18.794 \\ 4.900 \\ +\phantom{0}31.820 \\ \hline 91.184 \\ \hline \end{array}$

Hence, the sum is 91.184

Add:

63.05, 24.839, 3.7, 16.85

Answer

Maximum number of decimal places in given decimals is 3. So, we convert them into like decimals, each having 3 places of decimal, by annexing zeros.

Thus, we get: 63.050, 24.839, 3.700 and 16.850

On adding column-wise, we get:

$\begin{array}{r} 63.050 \\ 24.839 \\ 3.700 \\ +\phantom{0}16.850 \\ \hline 108.439 \\ \hline \end{array}$

Hence, the sum is 108.439

Subtract :

2.975 from 8.23

Answer

Converting the given decimals into like decimals, we have to subtract 2.975 from 8.230.

Subtracting columnwise, we get:

$\begin{array}{r} 8.230 \\ -\phantom{0}2.975 \\ \hline 5.255 \\ \hline \end{array}$

Hence, the answer is 5.255

Subtract :

0.75 from 1.3

Answer

Converting the given decimals into like decimals, we have to subtract 0.75 from 1.30.

Subtracting columnwise, we get:

$\begin{array}{r} 1.30 \\ -\phantom{0}0.75 \\ \hline 0.55 \\ \hline \end{array}$

Hence, the answer is 0.55

Subtract :

6.054 from 11.26

Answer

Converting the given decimals into like decimals, we have to subtract 6.054 from 11.260.

Subtracting columnwise, we get:

$\begin{array}{r} 11.260 \\ -\phantom{0}6.054 \\ \hline 5.206 \\ \hline \end{array}$

Hence, the answer is 5.206

Subtract :

134.68 from 201.3

Answer

Converting the given decimals into like decimals, we have to subtract 134.68 from 201.30.

Subtracting columnwise, we get:

$\begin{array}{r} 201.30 \\ -134.68 \\ \hline 66.62 \\ \hline \end{array}$

Hence, the answer is 66.62

Take out 6.345 from 8.1.

Answer

Converting the given decimals into like decimals, we have to subtract 6.345 from 8.100.

Subtracting columnwise, we get:

$\begin{array}{r} 8.100 \\ -\phantom{0}6.345 \\ \hline 1.755 \\ \hline \end{array}$

Hence, the answer is 1.755

What is the difference between 68.5 and 0.685?

Answer

Converting the given decimals into like decimals, we have to subtract 0.685 from 68.500.

Subtracting columnwise, we get:

$\begin{array}{r} 68.500 \\ -\phantom{0}0.685 \\ \hline 67.815 \\ \hline \end{array}$

Hence, the answer is 67.815

What is the excess of 90 over 53.865?

Answer

Converting the given decimals into like decimals, we have to subtract 53.865 from 90.000.

Subtracting columnwise, we get:

$\begin{array}{r} 90.000 \\ -53.865 \\ \hline 36.135 \\ \hline \end{array}$

Hence, the answer is 36.135

What should be subtracted from 50 to get 34.57?

Answer

Let the required number be x

50 - x = 34.57

x = 50 - 34.57

Converting the given decimals into like decimals, we have to subtract 34.57 from 50.00.

Subtracting columnwise, we get:

$\begin{array}{r} 50.00 \\ -34.57 \\ \hline 15.43 \\ \hline \end{array}$

Hence, the answer is 15.43

What should be added to 63.47 to get 91?

Answer

Let the required number be x

63.47 + x = 91

x = 91 - 63.47

Converting the given decimals into like decimals, we have to subtract 63.47 from 91.00.

Subtracting columnwise, we get:

$\begin{array}{r} 91.00 \\ -63.47 \\ \hline 27.53 \\ \hline \end{array}$

Hence, the answer is 27.53

Manish buys a ₹8.75 metro ticket with a ₹20 note. How much money does he get back?

Answer

Given:

Total money = ₹20.00

Cost of ticket = ₹8.75

Money received back = ?

∴ Money received back = (Total money) - (Cost of ticket)

Substituting the values in above, we get:

Money received back = ₹20.00 - ₹8.75

Converting the given decimals into like decimals, we have to subtract 8.75 from 20.00.

Subtracting columnwise, we get:

$\begin{array}{r} 20.00 \\ -\phantom{0}8.75 \\ \hline 11.25 \\ \hline \end{array}$

Hence, he gets back ₹11.25

A baby increases in weight from 5.58 kg to 6.16 kg. How much weight has the baby gained?

Answer

Given:

New weight = 6.16 kg

Previous weight = 5.58 kg

Weight gained = ?

∴ Weight gained = (New weight) - (Previous weight)

Substituting the values in above, we get:

Weight gained = 6.16 kg - 5.58 kg

Subtracting columnwise, we get:

$\begin{array}{r} 6.16 \\ -5.58 \\ \hline 0.58 \\ \hline \end{array}$

Hence, the baby has gained 0.58 kg

Simplify :

67 + 13.85 - 29.904

Answer

Given expression:

= 67 + 13.85 - 29.904
= 67.000 + 13.850 - 29.904 $\quad$ [Converting into like decimals]
= (67.000 + 13.850) - 29.904
= 80.850 - 29.904
= 50.546

$\begin{array}{r|r} 67.000 & 80.850 \\ +\phantom{0}13.850 & -\phantom{0}29.904 \\ \hline 80.850 & 50.946 \\ \hline \end{array}$

Hence, the answer is 50.946

Simplify :

16.753 + 4.06 - 13.89

Answer

Given expression:

= 16.753 + 4.06 - 13.89
= 16.753 + 4.060 - 13.890 $\quad$ [Converting into like decimals]
= (16.753 + 4.060) - 13.890
= 20.813 - 13.890
= 6.923

$\begin{array}{r|r} 16.753 & 20.813 \\ +\phantom{0}4.060 & -\phantom{0}13.890 \\ \hline 20.813 & 6.923 \\ \hline \end{array}$

Hence, the answer is 6.923

Simplify :

1 - 10.5 + 12.213

Answer

Given expression:

= 1 - 10.5 + 12.213
= 1.000 - 10.500 + 12.213 $\quad$ [Converting into like decimals]
= (1.000 + 12.213) - 10.500 $\quad$ [Rearranging terms]
= 13.213 - 10.500
= 2.713

$\begin{array}{r|r} 1.000 & 13.213 \\ +\phantom{0}12.213 & -\phantom{0}10.500 \\ \hline 13.213 & 2.713 \\ \hline \end{array}$

Hence, the answer is 2.713

Simplify :

81 - 15.68 - 4.2

Answer

Given expression:

= 81 - 15.68 - 4.2
= 81.00 - 15.68 - 4.20 $\quad$ [Converting into like decimals]
= (81.00) - (15.68 + 4.20) $\quad$ [Rearranging terms]
= 81.00 - 19.88
= 61.12

$\begin{array}{r|r} 15.68 & 81.00 \\ +\phantom{0}4.20 & -\phantom{0}19.88 \\ \hline 19.88 & 61.12 \\ \hline \end{array}$

Hence, the answer is 61.12

Simplify :

555 - 55.5 - 5.555

Answer

Given expression:

= 555 - 55.5 - 5.555
= 555.000 - 55.500 - 5.555 $\quad$ [Converting into like decimals]
= 555.000 - (55.500 + 5.555) $\quad$ [Rearranging terms]
= 555.000 - 61.055
= 493.945

$\begin{array}{r|r} 55.500 & 555.000 \\ +\phantom{0}5.555 & -\phantom{0}61.055 \\ \hline 61.055 & 493.945 \\ \hline \end{array}$

Hence, the answer is 493.945

Simplify :

100 - 32.5 - 46.74 - 12.925

Answer

Given expression:

= 100 - 32.5 - 46.74 - 12.925
= 100.000 - 32.500 - 46.740 - 12.925 $\quad$ [Converting into like decimals]
= 100.000 - (32.500 + 46.740 + 12.925) $\quad$ [Rearranging terms]
= 100.000 - 92.165
= 7.835

$\begin{array}{r|r|r} 32.500 & 79.240 & 100.000\ +\phantom{0}46.740 & +\phantom{0}12.925 & -\phantom{0}92.165 \\ \hline 79.240 & 92.165 & 7.835 \\ \hline \end{array}$

Hence, the answer is 7.835

Multiply :

6.5 x 10

Answer

We have:

6.5 x 10

On multiplying 6.5 by 10, the decimal point is shifted by one place to the right.

∴ 6.5 × 10 = 65

Multiply :

0.8 x 10

Answer

We have:

0.8 x 10

On multiplying 0.8 by 10, the decimal point is shifted by one place to the right.

∴ 0.8 × 10 = 8

Multiply :

9.07 x 10

Answer

We have:

9.07 x 10

On multiplying 9.07 by 10, the decimal point is shifted by one place to the right.

∴ 9.07 × 10 = 90.7

Multiply :

2.345 x 10

Answer

We have:

2.345 x 10

On multiplying 2.345 by 10, the decimal point is shifted by one place to the right.

∴ 2.345 × 10 = 23.45

Multiply :

4.63 x 100

Answer

We have:

4.63 x 100

On multiplying 4.63 by 100, the decimal point is shifted by two places to the right.

∴ 4.63 × 100 = 463

Multiply :

8.279 x 100

Answer

We have:

8.279 x 100

On multiplying 8.279 by 100, the decimal point is shifted by two places to the right.

∴ 8.279 × 100 = 827.9

Multiply :

7.8 x 100

Answer

We have:

7.8 x 100

On multiplying 7.8 by 100, the decimal point is shifted by two places to the right.

7.80 x 100 = 780

∴ 7.8 × 100 = 780

Multiply :

0.09 x 100

Answer

We have:

0.09 x 100

On multiplying 0.09 by 100, the decimal point is shifted by two places to the right.

∴ 0.09 × 100 = 9

Multiply :

0.283 x 1000

Answer

We have:

0.283 x 1000

On multiplying 0.283 by 1000, the decimal point is shifted by three places to the right.

∴ 0.283 × 1000 = 283

Multiply :

6.25 x 1000

Answer

We have:

6.25 x 1000

On multiplying 6.25 by 1000, the decimal point is shifted by three places to the right.

∴ 6.25 × 1000 = 6250

Multiply :

5.4 x 1000

Answer

We have:

5.4 x 1000

On multiplying 5.4 by 1000, the decimal point is shifted by three places to the right.

∴ 5.4 × 1000 = 5400

Multiply :

0.3 x 1000

Answer

We have:

0.3 x 1000

On multiplying 0.3 by 1000, the decimal point is shifted by three places to the right.

∴ 0.3 × 1000 = 300

Multiply :

2.4 x 16

Answer

We have:

24 x 16 = 384

∴ 2.4 × 16 = 38.4 $\hspace{2cm}$[1 place of decimal]

The answer is 38.4

Multiply :

3.45 x 17

Answer

We have:

345 × 17 = 5865

∴ 3.45 × 17 = 58.65 $\hspace{2cm}$[2 places of decimal]

The answer is 58.65

Multiply :

0.86 x 14

Answer

We have:

86 × 14 = 1204

∴ 0.86 × 14 = 12.04 $\hspace{2cm}$[2 places of decimal]

The answer is 12.04

Multiply :

2.68 x 30

Answer

We have:

268 × 30 = 8040

∴ 2.68 × 30 = 80.4 $\hspace{2cm}$[2 places of decimal]

The answer is 80.4

Multiply :

0.023 x 65

Answer

We have:

23 × 65 = 1495

∴ 0.023 × 65 = 1.495 $\hspace{2cm}$[3 places of decimal]

The answer is 1.495

Multiply :

0.0006 x 15

Answer

We have:

6 × 15 = 90

∴ 0.0006 × 15 = 0.009 $\hspace{2cm}$[4 places of decimal]

The answer is 0.009

Find the product :

5.6 x 1.4

Answer

First we multiply 56 by 14

$\begin{matrix} & & 5 & 6 \\ \times & & 1 & 4 \\ \hline & 2 & 2 & 4 \\ & 5 & 6 & \times \\ \hline & \bold{7} & \bold{8} & \bold{4} \end{matrix}$

Clearly, 56 × 14 = 784

Sum of decimal places in given decimals = (1 + 1) = 2

So, the product contains 2 places of decimal

∴ 5.6 × 1.4 = 7.84

Find the product :

2.35 x 7.2

Answer

First we multiply 235 by 72

$\begin{matrix} & & 2 & 3 & 5 \\ \times & & & 7 & 2 \\ \hline & & 4 & 7 & 0 \\ 1 & 6 & 4 & 5 & \times \\ \hline \bold{1} & \bold{6} & \bold{9} & \bold{2} & \bold{0} \end{matrix}$

Clearly, 235 × 72 = 16920

Sum of decimal places in given decimals = (2 + 1) = 3

So, the product contains 3 places of decimal

∴ 2.35 × 7.2 = 16.920 = 16.92

Find the product :

0.37 x 0.26

Answer

First we multiply 37 by 26

$\begin{matrix} & & 3 & 7 \\ \times & & 2 & 6 \\ \hline & 2 & 2 & 2 \\ & 7 & 4 & \times \\ \hline & \bold{9} & \bold{6} & \bold{2} \end{matrix}$

Clearly, 37 × 26 = 962

Sum of decimal places in given decimals = (2 + 2) = 4

So, the product contains 4 places of decimal

∴ 0.37 × 0.26 = 0.0962

Find the product :

0.74 x 6.7

Answer

First we multiply 74 by 67

$\begin{matrix} & & & 7 & 4 \\ \times & & & 6 & 7 \\ \hline & & 5 & 1 & 8 \\ & 4 & 4 & 4 & \times \\ \hline & \bold{4} & \bold{9} & \bold{5} & \bold{8} \end{matrix}$

Clearly, 74 × 67 = 4958

Sum of decimal places in given decimals = (2 + 1) = 3

So, the product contains 3 places of decimal

∴ 0.74 × 6.7 = 4.958

Find the product :

5.64 x 0.08

Answer

First we multiply 564 by 8

$\begin{matrix} & & 5 & 6 & 4 \\ \times & & & & 8 \\ \hline & \bold{4} & \bold{5} & \bold{1} & \bold{2} \end{matrix}$

Clearly, 564 × 8 = 4512

Sum of decimal places in given decimals = (2 + 2) = 4

So, the product contains 4 places of decimal

∴ 5.64 × 0.08 = 0.4512

Find the product :

2.75 x 1.7

Answer

First we multiply 275 by 17

$\begin{matrix} & & 2 & 7 & 5 \\ \times & & & 1 & 7 \\ \hline & 1 & 9 & 2 & 5 \\ & 2 & 7 & 5 & \times \\ \hline & \bold{4} & \bold{6} & \bold{7} & \bold{5} \end{matrix}$

Clearly, 275 × 17 = 4675

Sum of decimal places in given decimals = (2 + 1) = 3

So, the product contains 3 places of decimal

∴ 2.75 × 1.7 = 4.675

Find the product :

0.04 x 0.36

Answer

First we multiply 4 by 36

$\begin{matrix} & & 3 & 6 \\ \times & & & 4 \\ \hline & \bold{1} & \bold{4} & \bold{4} \end{matrix}$

Clearly, 4 × 36 = 144

Sum of decimal places in given decimals = (2 + 2) = 4

So, the product contains 4 places of decimal

∴ 0.04 × 0.36 = 0.0144

Find the product :

34.2 x 1.86

Answer

First we multiply 342 by 186

$\begin{matrix} & & 3 & 4 & 2 \\ \times & & 1 & 8 & 6 \\ \hline & 2 & 0 & 5 & 2 \\ 2 & 7 & 3 & 6 & \times \\ 3 & 4 & 2 & \times & \times \\ \hline \bold{6} & \bold{3} & \bold{6} & \bold{1} & \bold{2} \end{matrix}$

Clearly, 342 × 186 = 63612

Sum of decimal places in given decimals = (1 + 2) = 3

So, the product contains 3 places of decimal

∴ 34.2 × 1.86 = 63.612

Find the product :

0.028 x 0.9

Answer

First we multiply 28 by 9

$\begin{matrix} & & 2 & 8 \\ \times & & & 9 \\ \hline & \bold{2} & \bold{5} & \bold{2} \end{matrix}$

Clearly, 28 × 9 = 252

Sum of decimal places in given decimals = (3 + 1) = 4

So, the product contains 4 places of decimal

∴ 0.028 × 0.9 = 0.0252

Find the product :

2.3 x 0.23 x 0.1

Answer

First we multiply 23 by 23 and then by 1

$\begin{matrix} & & 2 & 3 \\ \times & & 2 & 3 \\ \hline & & 6 & 9 \\ & 4 & 6 & \times \\ \hline & \bold{5} & \bold{2} & \bold{9} \end{matrix}$

Clearly, 23 × 23 × 1 = 529

Sum of decimal places in given decimals = (1 + 2 + 1) = 4

So, the product contains 4 places of decimal

529 x 1 = 529

∴ 2.3 × 0.23 × 0.1 = 0.0529

Find the product :

1.2 x 3.5 x 0.3

Answer

First we multiply 12 by 35 and then by 3

$\begin{matrix} & & 1 & 2 \\ \times & & 3 & 5 \\ \hline & & 6 & 0 \\ & 3 & 6 & \times \\ \hline & \bold{4} & \bold{2} & \bold{0} \end{matrix}$

∴ 12 × 35 = 420

$\begin{matrix} & & 4 & 2 & 0 \\ \times & & & & 3 \\ \hline & \bold{1} & \bold{2} & \bold{6} & \bold{0} \end{matrix}$

∴ 12 × 35 × 3 = 1260

Sum of decimal places in given decimals = (1 + 1 + 1) = 3

So, the product contains 3 places of decimal

∴ 1.2 × 3.5 × 0.3 = 1.260 = 1.26

Find the product :

0.6 x 1.5 x 0.7

Answer

First we multiply 6 by 15 and then by 7

$\begin{matrix} & 1 & 5 \\ \times & & 6 \\ \hline & \bold{9} & \bold{0} \end{matrix}$

∴ 6 × 15 = 90

$\begin{matrix} & 9 & 0 \\ \times & & 7 \\ \hline \bold{6} & \bold{3} & \bold{0} \end{matrix}$

∴ 6 × 15 x 7 = 630

Sum of decimal places in given decimals = (1 + 1 + 1) = 3

So, the product contains 3 places of decimal

∴ 0.6 × 1.5 × 0.7 = 0.630 = 0.63

Find the product :

0.2 x 0.2 x 0.02

Answer

First we multiply 2 by 2 and then by 2

$\begin{matrix} & 2 \\ \times & 2 \\ \hline & \bold{4} \end{matrix}$

∴ 2 × 2 = 4

$\begin{matrix} & 4 \\ \times & 2 \\ \hline & \bold{8} \end{matrix}$

∴ 2 × 2 x 2 = 8

Sum of decimal places in given decimals = (1 + 1 + 2) = 4

So, the product contains 4 places of decimal

∴ 0.2 × 0.2 × 0.02 = 0.0008

Find the product :

1.1 x 0.1 x 0.11

Answer

First we multiply 11 by 1 and then by 11

$\begin{matrix} & 1 & 1 \\ \times & & 1 \\ \hline & \bold{1} & \bold{1} \end{matrix}$

∴ 11 × 1 = 11

$\begin{matrix} & & 1 & 1 \\ \times & & 1 & 1 \\ \hline & & 1 & 1 \\ & 1 & 1 & \times \\ \hline & \bold{1} & \bold{2} & \bold{1} \end{matrix}$

∴ 11 × 1 x 11 = 121

Sum of decimal places in given decimals = (1 + 1 + 2) = 4

So, the product contains 4 places of decimal

∴ 1.1 × 0.1 × 0.11 = 0.0121

Find the product :

0.6 x 0.06 x 0.006

Answer

First we multiply 6 by 6 and then by 6

$\begin{matrix} & & 6 \\ \times & & 6 \\ \hline & \bold{3} & \bold{6} \end{matrix}$

∴ 6 × 6 = 36

$\begin{matrix} & 3 & 6 \\ \times & & 6 \\ \hline \bold{2} & \bold{1} & \bold{6} \end{matrix}$

∴ 6 × 6 × 6 = 216

Sum of decimal places in given decimals = (1 + 2 + 3) = 6

So, the product contains 6 places of decimal

∴ 0.6 × 0.06 × 0.006 = 0.000216

Evaluate :

(1.3)²

Answer

We have:

(1.3)² = 1.3 × 1.3

First we multiply 13 by 13

$\begin{matrix} & & 1 & 3 \\ \times & & 1 & 3 \\ \hline & & 3 & 9 \\ & 1 & 3 & \times \\ \hline & \bold{1} & \bold{6} & \bold{9} \end{matrix}$

∴ 13 × 13 = 169

Sum of decimal places in given decimals = (1 + 1) = 2

So, the product contains 2 places of decimal

∴ (1.3)² = 1.69

Evaluate :

(0.06)²

Answer

We have:

(0.06)² = 0.06 × 0.06

First we multiply 6 by 6

$\begin{matrix} & & 6 \\ \times & & 6 \\ \hline & \bold{3} & \bold{6} \end{matrix}$

∴ 6 × 6 = 36

Sum of decimal places in given decimals = (2 + 2) = 4

So, the product contains 4 places of decimal

∴ (0.06)² = 0.0036

Evaluate :

(0.2)³

Answer

We have:

(0.2)³ = 0.2 × 0.2 × 0.2

First we multiply 2 × 2 × 2

$\begin{matrix} & 2 \\ \times & 2 \\ \hline & \bold{4} \end{matrix}$

∴ 2 × 2 =4

$\begin{matrix} & 4 \\ \times & 2 \\ \hline & \bold{8} \end{matrix}$

∴ 2 × 2 × 2 = 8

Sum of decimal places in given decimals = (1 + 1 + 1) = 3

So, the product contains 3 places of decimal

∴ (0.2)³ = 0.008

Evaluate :

(0.8)³

Answer

We have:

(0.8)³ = 0.8 × 0.8 × 0.8

First we multiply 8 × 8 × 8

$\begin{matrix} & & 8 \\ \times & & 8 \\ \hline & \bold{6} & \bold{4} \end{matrix}$

∴ 8 × 8 = 64

$\begin{matrix} & 6 & 4 \\ \times & & 8 \\ \hline \bold{5} & \bold{1} & \bold{2} \end{matrix}$

∴ 8 × 8 × 8 = 512

Sum of decimal places in given decimals = (1 + 1 + 1) = 3

So, the product contains 3 places of decimal

∴ (0.8)³ = 0.512

The cost of one pen is ₹42.25. Find the cost of one dozen such pens.

Answer

Given:

Cost of 1 pen = ₹42.25

Number of pens = 1 dozen = 12 pens

The cost of 1 dozen pens = (Cost of 1 pen) x (Number of pens)

Substituting the values in above, we get:

The cost of 1 dozen pens = ₹42.25 x 12

Sum of the decimal places in given decimals = 2 + 0 = 2

So, the product contains 2 places of decimal.

$\begin{matrix} & & 4 & 2 & 2 & 5 \\ \times & & & & 1 & 2 \\ \hline & & 8 & 4 & 5 & 0 \\ & 4 & 2 & 2 & 5 & \times \\ \hline & \bold{5} & \bold{0} & \bold{7} & \bold{0} & \bold{0} \end{matrix}$

∴ ₹42.25 × 12 = ₹507.00 = ₹507

Hence, the cost of one dozen pens = ₹507

A car moves at a constant speed of 56.4 km per hour. How much distance does it cover in 3.5 hours?

Answer

Given:

Speed per hour = 56.4 km

Total time = 3.5 hours

Distance covered = ?

We know the formula,

Distance = Speed x Time

Substituting the values in above, we get:

Distance = 56.4 km x 3.5 hours

Sum of the decimal places in given decimals = 1 + 1 = 2

So, the product contains 2 places of decimal

$\begin{matrix} & & 5 & 6 & 4 \\ \times & & & 3 & 5 \\ \hline & 2 & 8 & 2 & 0 \\ 1 & 6 & 9 & 2 & \times \\ \hline \bold{1} & \bold{9} & \bold{7} & \bold{4} & \bold{0} \end{matrix}$

∴ 56.4 km × 3.5 hours = 197.40 km = 197.4 km

Hence, the distance covered by the car = 197.4 km

A room is 4.5 m long and 3.8 m broad. Calculate the area of the floor of the room.

Answer

Given:

Length of the room = 4.5 m

Breadth of the room = 3.8 m

Area of the floor = ?

The floor will be of rectangular shape

We know the formula,

Area = Length x Breadth

Substituting the values in above, we get:

Area = 4.5 m x 3.8 m

Sum of the decimal places in given decimals = 1 + 1 = 2

So, the product contains 2 places of decimal

$\begin{matrix} & & 4 & 5 \\ \times & & 3 & 8 \\ \hline & 3 & 6 & 0 \\ 1 & 3 & 5 & \times \\ \hline \bold{1} & \bold{7} & \bold{1} & \bold{0} \end{matrix}$

∴ 4.5 m × 3.8 m = 17.10 m² = 17.1 m²

Hence, the area of the floor = 17.1 m²

The cost of 1 litre of refined oil is ₹124.75. What is the cost of 6.2 litres of this oil?

Answer

Given:

Cost of 1 litre of refined oil = ₹124.75

Total quantity of oil = 6.2 litres

Cost of 6.2 litres of oil = ?

Cost of 6.2 litres of oil = (Cost of 1 litre) x (Total quantity)

Substituting the values in above, we get:

Cost of 6.2 litres of oil = (₹124.75) x (6.2 litres)

Sum of the decimal places in given decimals = 2 + 1 = 3

So, the product contains 3 places of decimal

$\begin{matrix} & & 1 & 2 & 4 & 7 & 5 \\ \times & & & & & 6 & 2 \\ \hline & & 2 & 4 & 9 & 5 & 0 \\ & 7 & 4 & 8 & 5 & 0 & \times \\ \hline & \bold{7} & \bold{7} & \bold{3} & \bold{4} & \bold{5} & \bold{0} \end{matrix}$

∴ 124.75 × 6.2 litres = ₹773.450 = ₹773.45

Hence, the cost of 6.2 litres of oil = ₹773.45

Divide :

2.8 ÷ 10

Answer

On dividing 2.8 by 10, the decimal point is shifted by one place to the left.

∴ 2.8 ÷ 10 = 0.28

Divide :

0.63 ÷ 10

Answer

On dividing 0.63 by 10, the decimal point is shifted by one place to the left.

∴ 0.63 ÷ 10 = 0.063

Divide :

3.05 ÷ 10

Answer

On dividing 3.05 by 10, the decimal point is shifted by one place to the left.

∴ 3.05 ÷ 10 = 0.305

Divide :

245.6 ÷ 100

Answer

On dividing 245.6 by 100, the decimal point is shifted by two places to the left.

∴ 245.6 ÷ 100 = 2.456

Divide :

0.9 ÷ 100

Answer

On dividing 0.9 by 100, the decimal point is shifted by two places to the left.

∴ 0.9 ÷ 100 = 0.009

Divide :

1.23 ÷ 100

Answer

On dividing 1.23 by 100, the decimal point is shifted by two place to the left.

∴ 1.23 ÷ 10 = 0.0123

Divide :

134.2 ÷ 1000

Answer

On dividing 134.2 by 1000, the decimal point is shifted by three places to the left.

∴ 134.2 ÷ 1000 = 0.1342

Divide :

23.4 ÷ 1000

Answer

On dividing 23.4 by 1000, the decimal point is shifted by three places to the left.

∴ 23.4 ÷ 1000 = 0.0234

Divide :

0.7 ÷ 1000

Answer

On dividing 0.7 by 1000, the decimal point is shifted by three places to the left.

∴ 0.7 ÷ 1000 = 0.0007

Divide :

20.79 ÷ 9

Answer

On dividing 20.79 by 9, we get:

$\begin{array}{r} 2.31 \\ 9 \overline{\smash{)} 20.79 } \\ \underline{18}\phantom{.00} \\ 27\phantom{0} \\ \underline{27}\phantom{0} \\ 09 \\ \underline{09} \\ 0 \phantom{.} \end{array}$

Hence, 20.79 ÷ 9 = 2.31

Divide :

78.48 ÷ 12

Answer

On dividing 78.48 by 12, we get:

$\begin{array}{r} 6.54 \\ 12 \overline{\smash{)} 78.48 } \\ \underline{72}\phantom{.00} \\ 64\phantom{0} \\ \underline{60}\phantom{0} \\ 048 \\ \underline{048} \\ 0 \phantom{.} \end{array}$

Hence, 78.48 ÷ 12 = 6.54

Divide :

142.8 ÷ 21

Answer

On dividing 142.8 by 21, we get:

$\begin{array}{r} 6.8 \\ 21 \overline{\smash{)} 142.8 } \\ \underline{126}\phantom{.0} \\ 168 \\ \underline{168} \\ 0 \phantom{.} \end{array}$

Hence, 142.8 ÷ 21 = 6.8

Divide :

6.02 ÷ 7

Answer

On dividing 6.02 by 7, we get:

$\begin{array}{r} 0.86 \\ 7 \overline{\smash{)} 6.02 } \\ \underline{0}\phantom{.00} \\ 60\phantom{1} \\ \underline{56}\phantom{0} \\ 042 \\ \underline{042} \\ 0 \phantom{.} \end{array}$

Hence, 6.02 ÷ 7 = 0.86

Divide :

0.688 ÷ 8

Answer

On dividing 0.688 by 8, we get:

$\begin{array}{r} 0.086 \\ 8 \overline{\smash{)} 0.688 } \\ \underline{0}\phantom{.000} \\ 68\phantom{0} \\ \underline{64}\phantom{0} \\ 48 \\ \underline{48} \\ 0 \phantom{.} \end{array}$

Hence, 0.688 ÷ 8 = 0.086

Divide :

0.125 ÷ 25

Answer

On dividing 0.125 by 25, we get:

$\begin{array}{r} 0.005 \\ 25 \overline{\smash{)} 0.125 } \\ \underline{0}\phantom{.000} \\ 125 \\ \underline{125} \\ 0 \phantom{.} \end{array}$

Hence, 0.125 ÷ 25 = 0.005

Divide :

0.992 ÷ 31

Answer

On dividing 0.992 by 31, we get:

$\begin{array}{r} 0.032 \\ 31 \overline{\smash{)} 0.992 } \\ \underline{0}\phantom{.000} \\ 99\phantom{0} \\ \underline{93}\phantom{0} \\ 62 \\ \underline{62} \\ 0 \phantom{.} \end{array}$

Hence, 0.992 ÷ 31 = 0.032

Divide :

0.1728 ÷ 72

Answer

On dividing 0.1728 by 72, we get:

$\begin{array}{r} 0.0024 \\ 72 \overline{\smash{)} 0.1728 } \\ \underline{0}\phantom{.0000} \\ 172\phantom{0} \\ \underline{144}\phantom{0} \\ 288 \\ \underline{288} \\ 0 \phantom{.} \end{array}$

Hence, 0.1728 ÷ 72 = 0.0024

Divide :

0.12749 ÷ 61

Answer

On dividing 0.12749 by 61, we get:

$\begin{array}{r} 0.00209 \\ 61 \overline{\smash{)} 0.12749 } \\ \underline{0}\phantom{.00000} \\ 127\phantom{00} \\ \underline{122}\phantom{00} \\ 549 \\ \underline{549} \\ 0 \phantom{.} \end{array}$

Hence, 0.12749 ÷ 61 = 0.00209

Divide :

2.24 ÷ 0.8

Answer

We have:

$\dfrac{2.24}{0.8} = \dfrac{2.24 \times 10}{0.8 \times 10} = \dfrac{22.4}{8}$

On dividing 22.4 by 8, we get:

$\begin{array}{r} 2.8 \\ 8 \overline{\smash{)} 22.4 } \\ \underline{16}\phantom{.0} \\ 64 \\ \underline{64} \\ 0 \phantom{.} \end{array}$

Hence, $\dfrac{2.24}{0.8} = \dfrac{22.4}{8} = 2.8$

Divide :

1.242 ÷ 1.8

Answer

We have:

$\dfrac{1.242}{1.8} = \dfrac{1.242 \times 10}{1.8 \times 10} = \dfrac{12.42}{18}$

On dividing 12.42 by 18, we get:

$\begin{array}{r} 0.69 \\ 18 \overline{\smash{)} 12.42 } \\ \underline{108\phantom{0}} \\ 162 \\ \underline{162} \\ 0 \phantom{.} \end{array}$

Hence, $\dfrac{1.242}{1.8} = \dfrac{12.42}{18} = 0.69$

Divide :

0.1575 ÷ 0.21

Answer

We have:

$\dfrac{0.1575}{0.21} = \dfrac{0.1575 \times 100}{0.21 \times 100} = \dfrac{15.75}{21}$

On dividing 15.75 by 21, we get:

$\begin{array}{r} 0.75 \\ 21 \overline{\smash{)} 15.75 } \\ \underline{147\phantom{0}} \\ 105 \\ \underline{105} \\ 0 \phantom{.} \end{array}$

Hence, $\dfrac{0.1575}{0.21} = \dfrac{15.75}{21} = 0.75$

Divide :

0.0144 ÷ 0.12

Answer

We have:

$\dfrac{0.0144}{0.12} = \dfrac{0.0144 \times 100}{0.12 \times 100} = \dfrac{1.44}{12}$.

On dividing 1.44 by 12, we get:

$\begin{array}{r} 0.12 \\ 12 \overline{\smash{)} 1.44 } \\ \underline{12\phantom{0}} \\ 024 \\ \underline{024} \\ 0 \phantom{.} \end{array}$

Hence, $\dfrac{0.0144}{0.12} = \dfrac{1.44}{12} = 0.12$

Divide :

0.0783 ÷ 0.9

Answer

We have:

$\dfrac{0.0783}{0.9} = \dfrac{0.0783 \times 10}{0.9 \times 10} = \dfrac{0.783}{9}$

On dividing 0.783 by 9, we get:

$\begin{array}{r} 0.087 \\ 9 \overline{\smash{)} 0.783 } \\ \underline{0.72}\phantom{0} \\ 0.063 \\ \underline{0.063} \\ 0 \phantom{.} \end{array}$

Hence, $\dfrac{0.0783}{0.9} = \dfrac{0.783}{9} = 0.087$

Divide :

0.1164 ÷ 0.012

Answer

We have:

$\dfrac{0.1164}{0.012} = \dfrac{0.1164 \times 1000}{0.012 \times 1000} = \dfrac{116.4}{12}$.

On dividing 116.4 by 12, we get:

$\begin{array}{r} 9.7 \\ 12 \overline{\smash{)} 116.4 } \\ \underline{108}\phantom{.0} \\ 84 \\ \underline{84} \\ 0 \phantom{.} \end{array}$

Hence, $\dfrac{0.1164}{0.012} = \dfrac{116.4}{12} = 9.7$

Divide :

0.068 ÷ 0.17

Answer

We have:

$\dfrac{0.068}{0.17} = \dfrac{0.068 \times 100}{0.17 \times 100} = \dfrac{6.8}{17}$.

On dividing 6.8 by 17, we get:

$\begin{array}{r} 0.4 \\ 17 \overline{\smash{)} 6.8 } \\ \underline{0}\phantom{.8} \\ 68 \phantom{.}\ \underline{68} \phantom{.}\ 0 \phantom{0} \end{array}$

Hence, $\dfrac{0.068}{0.17} = \dfrac{6.8}{17} = 0.4$

Divide :

0.02324 ÷ 0.28

Answer

We have:

$\dfrac{0.02324}{0.28} = \dfrac{0.02324 \times 100}{0.28 \times 100} = \dfrac{2.324}{28}$.

On dividing 2.324 by 28, we get:

$\begin{array}{r} 0.083 \\ 28 \overline{\smash{)} 2.324 } \\ \underline{224\phantom{0}} \\ 84 \\ \underline{84} \\ 0 \phantom{.} \end{array}$

Hence, $\dfrac{0.02324}{0.28} = \dfrac{2.324}{28} = 0.083$

Divide :

0.03822 ÷ 0.049

Answer

We have:

$\dfrac{0.03822}{0.049} = \dfrac{0.03822 \times 1000}{0.049 \times 1000} = \dfrac{38.22}{49}$.

On dividing 38.22 by 49, we get:

$\begin{array}{r} 0.78 \\ 49 \overline{\smash{)} 38.22 } \\ \underline{343} \phantom{0} \\ 392 \\ \underline{392} \\ 0 \phantom{.} \end{array}$

Hence, $\dfrac{0.03822}{0.049} = \dfrac{38.22}{49} = 0.78$

Simplify :

$\dfrac{1.3 \times 2.4}{0.39}$

Answer

We have:

$\phantom{=} \dfrac{1.3 \times 2.4}{0.39} = \dfrac{3.12}{0.39} = \dfrac{3.12 \times 100}{0.39 \times 100} = \dfrac{312}{39}$

On dividing 312 by 39, we get:

$\begin{array}{r} 8 \\ 39 \overline{\smash{)} 312 } \\ \underline{312} \\ 0 \end{array}$

Hence, the answer is 8.

Simplify :

$\dfrac{2.5 \times 40.4}{50}$

Answer

We have:

$\phantom{=} \dfrac{2.5 \times 40.4}{50} = \dfrac{101.0}{50} = \dfrac{101}{50}$

On dividing 101 by 50, we get:

$\begin{array}{r} 2.02 \\ 50 \overline{\smash{)} 101.00 } \\ \underline{100} \phantom{.00} \\ 10 \phantom{0} \\ \underline{00} \phantom{0} \\ 100 \\ \underline{100} \\ 0 \end{array}$

Hence, the answer is 2.02

Simplify :

$\dfrac{6.3}{0.3 \times 0.1}$

Answer

We have:

$\dfrac{6.3}{0.03} = \dfrac{6.3 \times 100}{0.03 \times 100} = \dfrac{630}{3}$

On dividing 630 by 3, we get:

$\begin{array}{r} 210 \\ 3 \overline{\smash{)} 630 } \\ \underline{6} \phantom{00} \\ 03 \phantom{0} \\ \underline{3} \phantom{0} \\ 00 \\ \underline{0} \\ 0 \end{array}$

Hence, the answer is 210

A boy bought 8 pencils for ₹46.80. What is the cost of each pencil?

Answer

Given:

Cost of 8 pencils = ₹46.80

Number of pencils = 8

Cost of each pencil = ?

Cost of each pencil = (Total Cost) ÷ (Number of pencils)

Substituting the values:

Cost of each pencil = ₹46.80 ÷ 8

On dividing 46.80 by 8, we get:

$\begin{array}{r} 5.85 \\ 8 \overline{\smash{)} 46.80 } \\ \underline{40} \phantom{.00} \\ 68 \phantom{0} \\ \underline{64} \phantom{0} \\ 040 \\ \underline{040} \\ 0 \end{array}$

46.80 ÷ 8 = 5.85

Hence, the cost of each pencil is ₹5.85

A car covers a distance of 276.75 km in 4.5 hours. What is the average speed of the car?

Answer

Given:

Distance = 276.75 km

Time = 4.5 hours

Speed = ?

We know the formula,

Speed = Distance ÷ Time

Substituting the values:

Speed = 276.75 km ÷ 4.5 hours

= $\dfrac{276.75 \times 10}{4.5 \times 10}$

= $\dfrac{2767.5}{45} \quad$ [Multiplying both sides by 10 to make denominator a whole number]

On dividing 2767.5 by 45, we get:

$\begin{array}{r} 61.5 \\ 45 \overline{\smash{)} 2767.5 } \\ \underline{270} \phantom{.00} \\ 67 \phantom{.0} \\ \underline{45} \phantom{.0} \\ 225 \\ \underline{225} \\ 0 \phantom{0} \end{array}$

276.75 ÷ 4.5 = 61.5

Hence, the average speed of the car is 61.5 km/h

2.25 m of a cloth costs ₹326.25. What is the cost of 1 m of cloth?

Answer

Given:

Total Cost = ₹326.25

Total length = 2.25 m

Cost of 1 m cloth = ?

Cost of 1 m cloth = (Total Cost) ÷ (Total length)

Substituting the values:

Cost of 1 m cloth = ₹326.25 ÷ 2.25 m

= $\dfrac{326.25 \times 100}{2.25 \times 100}$

= $\dfrac{32625}{225} \quad$ [Multiplying both sides by 100 to make denominator a whole number]

On dividing 32625 by 225, we get:

$\begin{array}{r} 145 \\ 225 \overline{\smash{)} 32625 } \\ \underline{225} \phantom{00} \\ 1012 \phantom{0} \\ \underline{900} \phantom{0} \\ 1125 \\ \underline{1125} \\ 0 \end{array}$

326.25 ÷ 2.25 = 145

Hence, the cost of 1 m of cloth is ₹145

The product of two numbers is 52.8. If one of them is 8.25, find the other.

Answer

Let p and q be two numbers

Given:

Product of two numbers = 52.8

One number = p = 8.25

Other number = q = ?

p x q = 52.8

Substituting the values:

8.25 x q = 52.8

q = 52.8 ÷ 8.25 $\quad$ [Solving for q]

= $\dfrac{52.8 \times 100}{8.25 \times 100}$

= $\dfrac{5280}{825} \quad$ [Multiplying both sides by 100 to make denominator a whole number]

On dividing 5280 by 825, we get:

$\begin{array}{r} 6.4 \\ 825 \overline{\smash{)} 5280.0 } \\ \underline{4950} \phantom{.0} \\ 330.0 \\ \underline{330.0} \\ 0 \end{array}$

52.8 ÷ 8.25 = 6.4

Hence, the other number is 6.4

How many equal pieces, each of length 3.6 cm can be cut from a rope of length 61.2 cm?

Answer

Given:

Total length of rope = 61.2 cm

Length of each piece = 3.6 cm

Number of pieces = ?

Number of pieces = (Total length) ÷ (Length of each piece)

Substituting the values:

Number of pieces = 61.2 cm ÷ 3.6 cm

$= \dfrac{61.2 \times 10}{3.6 \times 10} = \dfrac{612}{36}$

On dividing 612 by 36, we get:

$\begin{array}{r} 17 \\ 36 \overline{\smash{)} 612 } \\ \underline{36} \phantom{0} \\ 252 \\ \underline{252} \\ 0 \end{array}$

61.2 ÷ 3.6 = 17

Hence, 17 equal pieces can be cut from the rope.

Express the following as a recurring decimal:

$\dfrac{20}{3}$

Answer

By actual division, we get:

$\begin{array}{r} 6.666... \\ 3 \overline{\smash{)} 20.000 } \\ \underline{18} \phantom{.000} \\ 20 \phantom{.00} \\ \underline{18} \phantom{.00} \\ 20 \phantom{.0} \\ \underline{18} \phantom{.0} \\ 2 \phantom{.} \end{array}$