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RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7 PDF Download

Q.1. Convert each of the following into a fraction in its simplest form:
(i) .8

(ii) .75
(iii) .06
(iv) .285
Ans. 
We have:
(i) 0.8 = 8/10 = (8÷2) / 10÷2 = 4/5
(ii) 0.75 = 75/100 = (75÷25) / (100÷25) = 3/4
(iii) 0.06 = 6/100 = (6÷2) / (100÷2) =3/50
(iv) 0.285 = 285/1000 = (285÷5) / (1000÷5) =57/200

Q.2. Convert each of the following as a mixed fraction:
(i) 5.6

(ii) 12.25
(iii) 6.004
(iv) 4.625
Ans.
We have:
(i) 5.6 = 56/10 = (56÷2) / (10÷2) = 28/5 =RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
(ii) 12.25 = 1225/100 =(1225÷25) / 100÷25 = 49/4 =RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
(iii) 6.004= 6004/1000 = (6004÷4) / (1000÷4) = 1501/250 = RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
(iv) 4.625 = 4625/1000 =(4625÷125) / (1000÷125) = 37/8 =RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7 

Q.3. Convert each of the following into like decimals:
(i) 47/10
(ii) 156/100
(iii) 2516/100
(iv) 3524/1000

(v) 25/8
(vi)RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
(vii)RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
(viii) 17/20
Ans. 
(i) 47/10
On dividing, we get:
RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
∴ 47/10 = 4.7
(ii)  156/100
 On dividing, we get:
RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
∴156/100 = 1.56
(iii) 2516/100
On dividing, we get:
RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
∴ 2516/100 = 25.16
(iv) 3524/1000
On dividing, we get:
RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
∴ 3524/1000 = 3.524
(v) 25/8
On dividing, we get:
RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
∴ 25/8 = 3.125
(vi) RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7=17/5
On dividing, we get:
RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
∴ 17/5 = 3.4
(vii)RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7=52/25
On dividing, we get:
RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
∴ 52/25 = 2.08
(viii) 17/20
On dividing, we get:
RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7
∴ 17201720 = 0.85

Q.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
Ans.
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

Q.5. Fill in each of the place holders with the correct symbol > or <.
(i) 78.23RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 769.85

(ii) 3.406RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 73.46
(iii) 5.68RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 75.86
(iv) 14.05RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 714.005
(v) 1.85RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 71.805
(vi) 0.98RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 71.07
Ans. 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

Q.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
Ans.
(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.

Q.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
Ans.
(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.

Q.8. Express 45 mm in cm, m and km.
Ans.
45 mm = 45/10 cm = 4.5 cm
= 4.5 cm = 4.5/100 m = 0.045 m
= 0.045 m = 0.045/1000 km = 0.000045 km
∴ 45 mm = 4.5 cm = 0.045 m = 0.000045 km

Q.9. Express as rupees using decimals:
(i) 8 paise

(ii) 9 rupees 75 paise
(iii) 8 rupees 5 paise
Ans.
We have:
(i) 8 paise = Rs 8/100 = Rs 0.08
(ii) 9 rupees 75 paise = Rs (9+75/100) = Rs (9 + 0.75) = Rs 9.75
(iii) 8 rupees 5 paise  = Rs (8+ 5/100) = Rs (8 + 0.05) = Rs 8.05

Q.10. Express in km using decimals:
(i) 65 m

(ii) 284 m
(iii) 3 km 5 m
Ans. 
We have:
(i) 65 m = 65/1000 km = 0.065 km
∴ 65 m = 0.065 km
(ii) 284 m = 284/1000 km = 0.284 km
(iii) 3 km 5 m = (3+ 5/1000) = (3+ 0.005) = 3.005 km 

The document RS Aggarwal Solutions: Decimals (Exercise 3A) | Mathematics (Maths) Class 7 is a part of the Class 7 Course Mathematics (Maths) Class 7.
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FAQs on RS Aggarwal Solutions: Decimals (Exercise 3A) - Mathematics (Maths) Class 7

1. What are some common operations involving decimals?
Ans. Some common operations involving decimals include addition, subtraction, multiplication, and division. These operations are similar to those performed with whole numbers, but with decimals, it is important to align the decimal points before carrying out the calculations.
2. How can I add or subtract decimals?
Ans. To add or subtract decimals, align the decimal points and then perform the addition or subtraction as you would with whole numbers. If necessary, add zeros to the right of the decimal point to ensure the same number of decimal places in each term before carrying out the operation.
3. How do I multiply decimals?
Ans. To multiply decimals, multiply the numbers as if they were whole numbers, ignoring the decimal points. The product will have a decimal point placed such that the total number of decimal places in the factors is equal to the total number of decimal places in the product.
4. How do I divide decimals?
Ans. To divide decimals, first, divide the numbers as if they were whole numbers, ignoring the decimal points. Then, place the decimal point in the quotient by counting the total number of decimal places in the dividend and the divisor. The quotient will have the same number of decimal places as the total count.
5. How can I convert fractions to decimals?
Ans. To convert a fraction to a decimal, divide the numerator by the denominator. The result will be the decimal representation of the fraction. If the fraction is a recurring decimal, it can be represented using a bar over the repeating digits.
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