Chapter 9 - Decimal Fractions
Problem Set 36
Write the following mixed fractions in decimal form and read them aloud.
(1) 3 \(\large \frac {9}{10}\)
Ans:
3 \(\large \frac {9}{10}\) = 3.9
Read as: Three point nine
(2) 1 \(\large \frac {4}{10}\)
Ans:
1 \(\large \frac {4}{10}\) = 1.4
Read as: One point four
(3) 5 \(\large \frac {3}{10}\)
Ans:
5 \(\large \frac {3}{10}\) = 5.3
Read as: Five point three
(4) \(\large \frac {8}{10}\)
Ans:
\(\large \frac {8}{10}\) = 0.8
Read as: Zero point eight
(5) \(\large \frac {7}{10}\)
Ans:
\(\large \frac {7}{10}\) = 0.7
Read as: Zero point seven
Problem Set 37
Write the following mixed fractions in decimal form and read them aloud.
(1) 9 \(\large \frac {1}{10}\)
Ans:
9 \(\large \frac {1}{10}\) = 9.1
Read as: Nine point one
(2) 9 \(\large \frac {1}{100}\)
Ans:
9 \(\large \frac {1}{100}\) = 9.01
Read as: Nine point zero one
(3) 4 \(\large \frac {53}{100}\)
Ans:
4 \(\large \frac {53}{100}\) = 4.53
Read as: Four point five three
(4) \(\large \frac {78}{10}\)
Ans:
\(\large \frac {78}{10}\) = 0.78
Read as: Zero point seven eight
(5) \(\large \frac {5}{100}\)
Ans:
\(\large \frac {5}{100}\) = 0.05
Read as: Zero point zero five
(6) 5/10 \(\large \frac {5}{10}\)
Ans:
5/10 \(\large \frac {5}{10}\) = 0.5
Read as: Zero point five
(7) \(\large \frac {2}{10}\)
Ans:
\(\large \frac {2}{10}\) = 0.2
Read as: Zero point two
(8) \(\large \frac {20}{100}\)
Ans:
\(\large \frac {20}{100}\) = 0.2
Read as: Zero point two
Problem Set 38
Read the decimal fraction and write down the place value of each digit.
(1) 6.13
Ans:
Read as: Six point one three
Place value of 6 = 6 × 1 = 6
Place value of 1 = 1 × 0.1 = 0.1
Place value of 3 = 3 × 0.01 = 0.03
(2) 48.84
Ans:
Read as: Forty eight point eight four
Place value of 4 = 4 × 10 = 40
Place value of 8 = 8 × 1 = 8
Place value of 8 = 8 × 0.1 = 0.8
Place value of 4 = 4 × 0.01 = 0.04
(3) 72.05
Ans:
Read as: Seventy two point zero five
Place value of 7 = 7 × 10 = 70
Place value of 2 = 2 × 1 = 2
Place value of 0 = 0 × 0.1 = 0
Place value of 5 = 5 × 0.01 = 0.05
(4) 3.4
Ans:
Read as: Three point four.
Place value of 3 = 3 × 1 = 3
Place value of 4 = 4 × 0.1 = 0.4
(5) 0.59
Ans:
Read as: Zero point five nine
Place value of 0 = 0 × 1 = 0
Place value of 5 = 5 × 0.1 = 0.5
Place value of 9 = 9 × 0.01 = 0.09
Problem Set 39
1. Write how many rupees and how many paise.
(1) ₹ 58.43
Ans:
₹ 58.43 = 58 rupees 43 paise
(2) ₹ 9.30
Ans:
₹ 9.30 = 9 rupees 30 paise
(3) ₹ 2.30
Ans:
₹ 2.30 = 2 rupees 30 paise
(4) ₹ 2.3
Ans:
₹ 2.3 = 2 rupees 30 paise
2. Write how many rupees in decimal form.
(1) 6 rupees 25 paise
Ans:
6 rupees 25 paise = ₹ 6.25
(2) 15 rupees 70 paise
Ans:
15 rupees 70 paise = ₹ 15.70
(3) 8 rupees 5 paise
Ans:
8 rupees 5 paise = ₹ 8.05
(4) 22 rupees 4 paise
Ans:
22 rupees 4 paise = ₹ 22.04
(5) 720 paise
Ans:
720 paise = ₹ 7.20
3. Write how many metres and how many centimetres.
(1) 58.75 m
Ans:
58.75 m = 58 m 75 cm
(2) 9.30 m
Ans:
9.30 m = 9 m 30 cm
(3) 0.30 m
Ans:
0.30 m = 30 cm
(4) 0.3 m
Ans:
0.3 m = 30 cm
(5) 1.62 m
Ans:
1.62 m = 1 m 62 cm
(6) 91.4 m
Ans:
91.4 m = 91 cm 40 cm
(7) 7.02 m
Ans:
7.02 m = 7 m 2 cm
(8) 0.09 m
Ans:
0.09 m = 9 cm
4. Write how many metres in decimal form.
(1) 1 m 50 cm
Ans:
1 m 50 cm = 1.5 m
(2) 50 m 40 cm
Ans:
50 m 40 cm = 50.40 m
(3) 50 m 4 cm
Ans:
50 m 4 cm = 50.04 m
(4) 734 cm
Ans:
734 cm = 7.34 m
(5) 10 cm
Ans:
10 cm = 0.1 m
(6) 2 cm
Ans:
2 cm = 0.02 m
5. Write how many centimetres and how many millimetres.
(1) 6.9 cm
Ans:
6.9 cm = 6 cm 9 mm
(2) 20.4 cm
Ans:
20.4 cm = 20 cm 4 mm
(3) 0.8 cm
Ans:
0.8 cm = 8 mm
(4) 0.5 cm
Ans:
0.5 cm = 5 mm
6. Write how many centimetres in decimal form.
(1) 7 cm 1 mm
Ans:
7 cm 1 mm = 7.1 cm
(2) 16 mm
Ans:
16 mm = 1.6 cm
(3) 144 mm
Ans:
144 mm = 14.4 cm
(4) 8 mm
Ans:
8 mm = 0.8 cm
Problem Set 40
Write the following fractions as decimal fractions.
(1) Two and a half
Ans:
2 \(\large \frac {1}{2}\) = 2.5 = 2.50
(2) Two and a quarter
Ans:
2 \(\large \frac {1}{4}\) = 2.25
(3) Two and three quarters
Ans:
2 \(\large \frac {3}{4}\) = 2.75
(4) Ten and a half
Ans:
10 \(\large \frac {1}{2}\) = 10.5 = 10.50
(5) Fourteen and three quarters
Ans:
14 \(\large \frac {3}{4}\) = 14.75
(6) Sixteen and a quarter
Ans:
16 \(\large \frac {1}{4}\) = 18.25
Problem Set 41
1. Convert the following into decimal fractions and add them.
(1) ‘One and a half metre’ and ‘two and a half metres’
Solution:
One and a half metre = 1 \(\large \frac {1}{2}\) = 1.5 m
Two and a half metres = 2 \(\large \frac {1}{2}\) = 2.5 m
$$ \begin{array}{r}\overset11.5\\+\;2.5\\\hline4.0\end{array} $$
Ans: 1.5 + 2.5 = 4
(2) ‘Four and three quarter rupees’ and ‘seven and a quarter rupees’
Solution:
Four and three quarter rupees = \(\large \frac {1}{2}\) = 4.75 m
Seven and a quarter rupees = 7 \(\large \frac {1}{4}\) = 7.25 m
$$ \begin{array}{r}\overset14.\overset175\\+\;7.25\\\hline12.00\end{array} $$
Ans: 4.75 + 7.25 = 12
(3) ‘Six and a half metres’ and ‘three and three quarter metres’.
Ans:
Six and a half metres = 6 \(\large \frac {1}{2}\) = 6.5 m
Three and three quarter metres = 3 \(\large \frac {3}{4}\) = 3.75 m
$$ \begin{array}{r}\overset16.50\\+\;3.75\\\hline10.25\end{array} $$
Ans: 6.5 + 3.75 = 10.25
2. (1) 23.4 + 87.9
Solution:
$$ \begin{array}{r}\overset12\overset13.4\\+\;87.9\\\hline111.3\end{array} $$
Ans: 23.4 + 87.9 = 111.3
(2) 35.74 + 816.6
Solution:
$$ \begin{array}{r}\begin{array}{r}\overset13\overset15.74\\+\;816.60\\\hline852.34\end{array}\end{array} $$
Ans: 35.74 + 816.6 = 852.34
(3) 6.95 + 74.88
Solution:
$$ \begin{array}{r}\begin{array}{r}\overset1{}\overset16.\overset195\\+\;74.88\\\hline81.83\end{array}\end{array} $$
Ans: 6.95 + 74.88 = 81.83
(4) 41.03 + 9.98
Solution:
$$ \begin{array}{r}\begin{array}{r}\overset14\overset11.\overset103\\+\;9.98\\\hline51.01\end{array}\end{array} $$
Ans: 41.03 + 9.98 = 51.01
3. (1) 51.4 cm + 68.5 cm
Solution:
$$ \begin{array}{r}\begin{array}{r}51.4\;cm\\+\;68.5\;cm\\\hline119.9\;cm\end{array}\end{array} $$
Ans: 51.4 cm + 68.5 cm = 119.9 cm
(2) 94.7 m + 1738.45 m
Solution:
$$ \begin{array}{r}\begin{array}{r}\overset1{}\overset19\overset14.70\;m\\+\;1738.45\;m\\\hline1833.15\;m\end{array}\end{array} $$
Ans: 94.7 m + 1738.45 m = 1833.15 m
(3) ₹ 5158.75 + ₹ 841.25
Solution:
$$ \begin{array}{r}\begin{array}{r}₹\;\overset15\overset11\overset15\overset18.\overset175\\+\;₹\;\;\;841.25\\\hline6000.00\end{array}\end{array} $$
Ans: ₹ 5158.75 + ₹841.25 = 6000
Problem Set 42
1. Subtract the following :
(1) 25.74 – 13.42
Solution:
$$ \begin{array}{r}\,25.74\\-\,\;13.42\\\hline12.32\end{array} $$
Ans: 1.5 + 2.5 = 4
(2) 206.35 – 168.22
Solution:
$$ \begin{array}{c}\;\;\;\;\overset1{\require{cancel}\cancel2}\overset{\overset9{\require{cancel}\cancel{10}}}0\overset{16}{6\;}.\;3\;5\\-\,\:1\;\;6\;8\;.\;2\;2\\\hline\;\;\;\;0\;3\;8\;.\;1\;3\end{array} $$
Ans: 206.35 – 168.22 = 38.13
(3) 63.4 – 31.8
Solution:
$$ \begin{array}{c}\,\;\;\;\;\;\;6\overset2{\require{cancel}\cancel3}.\overset{14}{\require{cancel}\cancel4}\\-\;\,\;3\;1.\;8\\\hline\;\;\;\;\;\;3\;1.\;6\end{array} $$
Ans: 63.4 – 31.8 = 31.6
(4) 63.43 – 31.8
Solution:
$$\begin{array}{r}\,6\overset2{\cancel3}.\overset{14}{\cancel4}3\\-\,\;3\;1.\;8\;0\\\hline3\;1.\;6\;3\end{array} $$
Ans: 23.4 + 87.9 = 111.3
(5) 63.4 – 31.83
Solution:
$$ \begin{array}{r}\,6\overset2{\require{cancel}\cancel3}.\overset{\overset{12}{\require{cancel}\cancel3}}{\require{cancel}\cancel4}\overset{10}{\require{cancel}\cancel0}\\-\,\;3\;1\;.\;8\;\;3\\\hline3\;1\;.\;4\;\;7\end{array}$$
Ans: 35.74 + 816.6 = 852.34
(6) 8.23 – 5.45
Solution:
$$\begin{array}{r}\begin{array}{r}\;\overset7{\require{cancel}\cancel8}.\overset{\overset{11}{\require{cancel}\cancel{12}}}{\require{cancel}\cancel2}\overset{13}{\require{cancel}\cancel3}\\-\;5\;.\;4\;\;5\\\hline2\;.\;7\;\;8\end{array}\end{array}$$
Ans: 8.23 – 5.45 = 2.78
(7) 18.23 – 9.45
Solution:
$$ \begin{array}{r}\begin{array}{r}\require{cancel}\cancel1\overset{\overset{17}{\require{cancel}\cancel7}}{\require{cancel}\cancel8}.\overset{\overset{11}{\require{cancel}\cancel1}}{\require{cancel}\cancel2}\overset{13}{\require{cancel}\cancel3}\\-\;9\;.\;4\;\;5\\\hline8\;.\;7\;\;8\end{array}\end{array} $$
Ans: 18.23 – 9.45 = 8.78
(8) 78.03 – 41.65
Solution:
$$ \begin{array}{r}7\overset7{\require{cancel}\cancel8}.\overset{\overset9{\require{cancel}\cancel{10}}}{\require{cancel}\cancel0}\overset{13}{\require{cancel}\cancel3}\\-\,\;4\;1\;.\;6\;\;5\\\hline3\;6\;.\;3\;\;8\end{array} $$
Ans: 51.4 cm + 68.5 cm = 119.9 cm
2. Vrinda was 1.48 m tall. After a year, her height became 1.53 m. How many entimetres did her height increase in a year?
Solution:
Initial height of Vrinda = 1.48 m
Final height of Vrinda = 1.53 m
Increment in height in one year = ?
$$ \begin{array}{r}1.\overset4{\cancel5}\overset{13}{\cancel3}\\-\,\;1.\;4\;\,8\\\hline0.\;0\;\,5\end{array} $$
Now,
1 m = 100 cm
∴ 0.05 m = 0.05 × 100 cm = 5 cm
Ans: Vrinda’s height increased by 5 cm in a year.