Decimals - Exercise 3(C)

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.

∴ 7.8 × 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 $\quad$ [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 $\quad$ [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 $\quad$ [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 $\quad$ [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 $\quad$ [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 $\quad$ [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