RS Aggarwal 2019,2020 solution class 7 chapter 3 Decimals Exercise 3A

Exercise 3A

Page-39

Question 1:

Convert each of the following into a fraction in its simplest form:

(i) .8
(ii) .75
(iii) .06
(iv) .285

Answer 1:

We have:

(i) $0.8=\frac{8}{10}=\frac{8÷2}{10÷2}=\frac{4}{5}$

(ii) $0.75=\frac{75}{100} = \frac{75÷25}{100÷25}=\frac{3}{4}$

(iii) $0.06=\frac{6}{100}=\frac{6÷2}{100÷2}=\frac{3}{50}$

(iv) $0.285=\frac{285}{1000}=\frac{285÷5}{1000÷5}=\frac{57}{200}$

Question 2:

Convert each of the following as a mixed fraction:

(i) 5.6
(ii) 12.25
(iii) 6.004
(iv) 4.625

Answer 2:

We have:

 (i) $5.6=\frac{56}{10}=\frac{56÷2}{10÷2}=\frac{28}{5}=5\frac{3}{5}$

(ii) $12.25=\frac{1225}{100}=\frac{1225÷25}{100÷25}=\frac{49}{4}=12\frac{1}{4}$

(iii) $6.004=\frac{6004}{1000}=\frac{6004÷4}{1000÷4}=\frac{1501}{250}=6\frac{1}{250}$

(iv) $4.625=\frac{4625}{1000}=\frac{4625÷125}{1000÷125}=\frac{37}{8}=4\frac{5}{8}$

Question 3:

Convert each of the following into like decimals:

(i) $\frac{47}{10}$
(ii) $\frac{156}{100}$
(iii) $\frac{2516}{100}$
(iv) $\frac{3524}{1000}$
(v) $\frac{25}{8}$
(vi) $3\frac{2}{5}$
(vii) $2\frac{2}{25}$
(viii) $\frac{17}{20}$

Answer 3:

(i) $\frac{47}{10}$ 
    On dividing, we get:

   
    ∴ $\frac{47}{10}$ = 4.7

(ii)  $\frac{156}{100}$
 On dividing, we get:

       
∴$\frac{156}{100}$ = 1.56

(iii) $\frac{2516}{100}$
 On dividing, we get:


∴ $\frac{2516}{100}$ = 25.16

(iv) $\frac{3524}{1000}$
    
  On dividing, we get:


∴ $\frac{3524}{1000}$ = 3.524

(v) $\frac{25}{8}$
On dividing, we get:


∴ $\frac{25}{8}$ = 3.125

(vi) $3\frac{2}{5}=\frac{17}{5}$
  On dividing, we get:


∴ $\frac{17}{5}$ = 3.4

(vii) $2\frac{2}{25}=\frac{52}{25}$
        On dividing, we get:

        
∴ $\frac{52}{25}$ = 2.08

(viii) $\frac{17}{20}$

       On dividing, we get:

      

       ∴ $\frac{17}{20}$ = 0.85

Question 4:

Convert each of the following into like decimals:

(i) 6.5, 16.03, 0.274, 119.4
(ii) 3.5, 0.67, 15.6, 4

Answer 4:

Converting the given decimals into like decimals, we have:
(i) 6.500, 16.030, 0.274 and 119.400
(ii) 3.50, 0.67, 15.60 and 4.00

Question 5:

Fill in each of the place holders with the correct symbol > or <.

(i) 78.23 $\boxed{ }$ 69.85
(ii) 3.406 $\boxed{ }$ 3.46
(iii) 5.68 $\boxed{ }$ 5.86
(iv) 14.05 $\boxed{ }$ 14.005
(v) 1.85 $\boxed{ }$ 1.805
(vi) 0.98 $\boxed{ }$ 1.07

Answer 5:

We have,

(i) Comparing the whole number part, 78 > 69.
Thus, 78.23  > 69.85

(ii) Converting the decimals into like decimals, we get 3.406  and 3.460.
Comparing the whole number parts, 3 = 3
Comparing the tenths digit, 4 = 4
Comparing the hundredths digit, 6 > 0
Thus, 3.406  < 3.46

(iii)  Comparing the whole number parts, 5 = 5
Comparing the tenths digit, 6 <  8
Thus, 5.68  < 5.86

(iv) Converting the decimals into like decimals, we get 14.050 and 14.005.
Comparing the whole number parts, 14 = 14
Comparing the tenths digit, 0 = 0
Comparing the hundredths digit, 5 > 0
Thus,  14.05  > 14.005

(v) Converting the decimals into like decimals, we get 1.850 and 1.805.
Comparing the whole number parts, 1 = 1
Comparing the tenths digit, 8 = 8
Comparing the hundredths digit, 5 > 0
Thus, 1.85 > 1.805

(vi)  Comparing the whole number parts, 0 < 1
Thus, 0.98 < 1.07

Question 6:

Arrange the following decimals in ascending order:

(i) 4.6, 7.4, 4.58, 7.32, 4.06
(ii) 0.5, 5.5, 5.05, 0.05, 5.55
(iii) 6.84, 6.48, 6.8, 6.4, 6.08
(iv) 2.2, 2.202, 2.02, 22.2, 2.002

Answer 6:

(i) Converting the given decimals into like decimals, we get:
     4.60, 7.40, 4.58, 7.32, 4.06
     Clearly, 4.06 < 4.58 < 4.60 < 7.32 < 7.40
     Hence, the given decimals in ascending order are 4.06, 4.58, 4.6, 7.32 and 7.4.

(ii) Converting the given decimals into like decimals, we get:
      0.50, 5.50, 5.05, 0.05, 5.55
      Clearly, 0.05 < 0.50 < 5.05< 5.50 < 5.55
      Hence, the given decimals in ascending order are 0.05, 0.5, 5.05, 5.5 and 5.55.

(iii) Converting the given decimals into like decimals, we get:
        6.84, 6.48, 6.80, 6.40, 6.08
        Clearly, 6.08 < 6.40 < 6.48 < 6.80< 6.84
        Hence, the given decimals in ascending order are 6.08, 6.4, 6.48, 6.8 and 6.84.

(iv)  Converting the given decimals into like decimals, we get:
        2.200, 2.202, 2.020, 22.200, 2.002
        Clearly, 2.002 < 2.020 < 2.200 < 2.202 < 22.200
        Hence, the given decimals in ascending order are 2.002, 2.02, 2.2, 2.202 and 22.2.

Question 7:

Arrange the following decimals in descending order:

(i) 7.4, 8.34, 74.4, 7.44, 0.74
(ii) 2.6, 2.26, 2.06, 2.007, 2.3

Answer 7:

(i) Converting the given decimals into like decimals, we get:
     7.40, 8.34, 74.40, 7.44, 0.74
     Clearly, 74.40 > 8.34 > 7.44 > 7.40 > 0.74
     Hence, the given decimals in descending order are 74.4, 8.34, 7.44, 7.4 and 0.74.

(ii) Converting the given decimals into like decimals, we get:
      2.600, 2.260, 2.060, 2.007, 2.300
      Clearly, 2.600 > 2.300 > 2.260 > 2.060 > 2.007
      Hence, the given decimals in descending order are 2.6, 2.3, 2.26, 2.06 and 2.007.

Question 8:

Express 45 mm in cm, m and km.

Answer 8:

45 mm = $\frac{45}{10}$ cm = 4.5 cm

            = 4.5 cm = $\frac{4.5}{100} \mathrm{m}$ = 0.045 m

            = 0.045 m = $\frac{0.045}{1000} \mathrm{km}$ = 0.000045 km

∴ 45 mm = 4.5 cm = 0.045 m = 0.000045 km

Question 9:

Express as rupees using decimals:

(i) 8 paise
(ii) 9 rupees 75 paise
(iii) 8 rupees 5 paise

Answer 9:

We have:
(i) 8 paise = Rs $\frac{8}{100}$ = Rs 0.08

(ii) 9 rupees 75 paise = Rs $\left(9+\frac{75}{100}\right) = \mathrm{Rs} (9 + 0.75)$ = Rs 9.75

(iii) 8 rupees 5 paise  = $\mathrm{Rs} \left(8+ \frac{5}{100}\right) = \mathrm{Rs} (8 + 0.05)$= Rs 8.05

Question 10:

Express in km using decimals:

(i) 65 m
(ii) 284 m
(iii) 3 km 5 m

Answer 10:

We have:

(i) 65 m = $\frac{65}{1000}$ km = 0.065 km
     ∴ 65 m = 0.065 km

(ii) 284 m = $\frac{284}{1000}$km = 0.284 km

(iii) 3 km 5 m = $\left(3+ \frac{5}{1000}\right) = \left(3+ 0.005\right) = 3.005 \mathrm{km}$