Decimals - Exercise 3(D)

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.