RS Aggarwal 2021-2022 for Class 6 Maths Solutions Chapter 7- Decimal
RS Aggarwal Class 6 Math Solution Chapter 7- Decimal Exercise 7A is available here. RS Aggarwal Class 6 Math Solutions are solved by expert teachers in step by step, which help the students to understand easily. RS Aggarwal textbooks are responsible for a strong foundation in Maths. These textbook solutions help students in exams as well as their daily homework routine. The solutions included are easy to understand, and each step in the solution is described to match the students’ understanding.
Rs Aggarwal Class 6 Math Solution Chapter 7- Decimal
Exercise 7A
1. Write each of the following in figures:
(i) Fifty-eight point six three
(ii) One hundred twenty-four point four two five
(iii) Seven point seven six
(iv) Nineteen point eight
(v) Four hundred four point zero four four
(vi) Point one seven three
(vii) Point zero one five
Solution:
(i) 58.63
(ii) 124.425
(iii) 7.76
(iv) 19.8
(v) 404.044
(vi) 0.173
(vii) 0.015
2. Write the place value of each digit in each of the following decimals:
(i) 14.83
(ii) 275.269
(iii) 46.075
(iv) 302.459
(v) 5370.34
(vi) 186.209
Solution:
(i) In 14.83, we have:
Place value of 1 = 1 tens = 10
Place value of 4 = 4 ones = 4
Place value of 8 = 8 tenths = `frac\{8}{10}`
Place value of 3 = 3 hundredths = `frac\{3}{100}` (ii) In 275.269, we have:
Place value of 2 = 2 hundreds = 200
Place value of 7 = 7 tens = 70
Place value of 5 = 5 ones = 5
Place value of 2 = 2 tenths = `frac\{2}{10}`
Place value of 6 = 6 hundredths = `frac\{6}{100}`
Place value of 9 = 9 thousandths = `frac\{9}{1000}`
(iii) In 46.075, we have:
Place value of 4 = 4 tens = 40
Place value of 6 = 6 ones = 6
Place value of 0 = 0 tenths = `frac\{0}{10}` = 0
Place value of 7 = 7 hundredths = `frac\{7}{100}`
Place value of 5 = 5 thousandths = `frac\{5}{1000}` (iv) In 302.459, we have:
Place value of 3 = 3 hundreds = 300
Place value of 0 = 0 tens = 0
Place value of 2 = 2 ones = 2
Place value of 4 = 4 tenths = `frac\{4}{10}`
Place value of 5 = 5 hundredths = `frac\{5}{100}`
Place value of 9 = 9 thousandths = `frac\{9}{1000}` (v) In 5370.34, we have:
Place value of 5 = 5 thousands = 5000
Place value of 3 = 3 hundreds = 300
Place value of 7 = 7 tens = 70
Place value of 0 = 0 ones = 0
Place value of 3 = 3 tenths = `frac\{3}{10}`
Place value of 4 = 4 hundredths = `frac\{4}{100}` (vi) In 186.209, we have:
Place value of 1 = 1 hundreds = 100
Place value of 8 = 8 tens = 80
Place value of 6 = 6 ones = 6
Place value of 2 = 2 tenths = `frac\{2}{10}`
Place value of 0 = 0 hundredths = 0
Place value of 9 = 9 thousandths = `frac\{9}{1000}`
3. Write each of the following decimals in expanded form:
(i) 67.83
(ii) 283.61
(iii) 24.675
(iv) 0.294
(v) 8.006
(vi) 4615.72
Solution:
(i) 67.83 = 6 tens + 7 ones + 8 tenths + 3 hundredths
= 60 + 7 + `frac\{8}{10}` + `frac\{3}{100}` (ii) 283.61 = 2 hundreds + 8 tens + 3 ones + 6 tenths + 1 hundredths
= 200 + 80 + 3 + `frac\{6}{10}` + `frac\{1}{100}` (iii) 24.675 = 2 tens + 4 ones + 6 tenths + 7 hundredths + 5 thousandths
= 20 + 4 + `frac\{6}{10}` + `frac\{7}{100}` + `frac\{5}{1000}` (iv) 0.294 = 2 tenths + 9 hundredths + 4 thousandths
= `frac\{2}{10}` + `frac\{9}{100}` + `frac\{4}{1000}` (v) 8.006 = 8 ones + 0 tenths + 0 hundredths + 6 thousandths
= 8 + `frac\{0}{10}` + `frac\{0}{100}` + `frac\{6}{1000}` (vi) 4615.72 = 4 thousands + 6 hundreds + 1 tens + 5 ones + 7 tenths + 2 hundredths
= 4000 + 600 + 10 + 5 + `frac\{7}{10}` + `frac\{2}{100}`
4. Write each of the following in decimal form:
(i) 40 + 6 + `frac\{7}[10}` + `frac\{9}[100}`
(ii) 500 + 70 + 8 + `frac\{3}[10}` + `frac\{1}[100}` + `frac\{6}[1000}`
(iii) 700 + 30 + 1 + `frac\{8}[10}` + `frac\{4}[100}`
(iv) 600 + 5 + `frac\{7}[100}` + `frac\{9}[1000}`
(v) 800 + 5 + `frac\{8}[10}` + `frac\{6}[1000}`
(vi) 30 + 9 + `frac\{4}[100}` + `frac\{8}[1000}`
Solution:
(i) 40 + 6 + `frac\{7}[10}` + `frac\{9}[100}`
= 46 + 0.7 + .09 = 46.79 (ii) 500 + 70 + 8 + `frac\{3}[10}` + `frac\{1}[100}` + `frac\{6}[1000}`
= 578 + 0.3 + 0.01 + 0.006 = 578.316 (iii) 700 + 30 + 1 + `frac\{8}[10}` + `frac\{4}[100}`
= 731 + 0.8 + 0.04 = 731.84 (iv) 600 + 5 + `frac\{7}[100}` + `frac\{9}[1000}`
= 605 + 0.07 + 0.009 = 605.079 (v) 800 + 5 + `frac\{8}[10}` + `frac\{6}[1000}`
= 805 + 0.8 + 0.006 = 805.806 (vi) 30 + 9 + `frac\{4}[100}` + `frac\{8}[1000}`
= 39 + 0.04 + 0.008 = 39.048
5. Convert each of the following into like decimals:
(i) 7.5, 64.23, 0.074 (ii) 0.6, 5.937, 2.36, 4.2
(iii) 1.6, 0.07, 3.58, 2.9 (iv) 2.5, 0.63, 14.08, 1.637
Solution:
(i) 0.074 has maximum 3 decimal places. So, we convert other given number into 3 decimal places by adding zeroes to the extreme right of the decimal part.
So, Required like decimals = 7.500, 64.230, 0.074
(ii) 5.937 has maximum 3 decimal places. So, we convert other given number into 3 decimal places by adding zeroes to the extreme right of the decimal part.
So, Required like decimals = 0.600, 5.937, 2.360, 4.200
(iii) 0.07 and 3.58 has maximum 2 decimal places. So, we convert other given number into 2 decimal places by adding zeroes to the extreme right of the decimal part.
So, Required like decimals = 1.60, 0.07, 3.58, 2.90
(iv) 1.637 has maximum 3 decimal places. So, we convert other given number into 3 decimal places by adding zeroes to the extreme right of the decimal part.
So, Required like decimals = 2.500, 0.630, 14.080, 1.637
6. Fill in each of the place holders with the correct symbol > or < :
(i) 84.23 ⬜ 76.35 (ii) 7.608 ⬜ 7.68
(iii) 8.34 ⬜ 8.43 (iv) 12.06 ⬜ 12.006
(v) 3.85 ⬜ 3.805 (vi) 0.97 ⬜ 1.07
Solution:
(i) 84.23 > 76.35
∵ 84 is greater than 76. Therefore, 84.23 is greater than 76.35.
(ii) 7.608 < 7.68
In 7.608, hundredths place is 0 and In 7.68, hundredths place is 8.
∵ 0 < 8
So, 7.68 is greater than 7.608
(iii) 8.34 < 8.43
In 8.34, tenths place is 3 and In 8.43, tenths place is 4.
∵ 3 < 4
So, 8.43 is greater than 8.34
(iv) 12.06 > 12.006
In 12.06, hundredths place is 6 and In 12.006, hundredths place is 0.
∵ 6 > 0
So, 12.06 is greater than 12.006
(v) 3.85 > 3.805
In 3.85, hundredths place is 5 and In 3.805, hundredths place is 0.
∵ 5 > 0
So, 3.85 is greater than 3.805
(vi) 0.97 < 1.07
∵ 1 is greater than 0. Therefore, 1.07 is greater than 0.97.
7. Arrange the following decimals in an ascending order:
(i) 5.8, 7.2, 5.69, 7.14, 5.06
(ii) 0.6, 6.6, 6.06, 66.6, 0.06
(iii) 6.54, 6.45, 6.4, 6.5, 6.05
(iv) 3.3, 3.303, 3.033, 0.33, 3.003
Solution:
First we will convert them into like decimals. After that we arrange them into ascending order.
(i) 5.8, 7.2, 5.69, 7.14, 5.06
= 5.80, 7.20, 5.69, 7.14, 5.06
Clearly, 5.06 < 5.69 < 5.80 < 7.14 < 7.20 Hence, the given decimals can be arranged in the ascending order as follows: 5.06, 5.69, 5.8, 7.14 and 7.2
(ii) 0.6, 6.6, 6.06, 66.6, 0.06
= 0.60, 6.60, 6.06, 66.60, 0.06
Clearly, 0.06 < 0.60 < 6.06 < 6.60 < 66.60 Hence, the given decimals can be arranged in the ascending order as follows: 0.06, 0.60, 6.06, 6.60 and 66.60
(iii) 6.54, 6.45, 6.4, 6.5, 6.05
= 6.54, 6.45, 6.40, 6.50, 6.05
Clearly, 6.05 < 6.40 < 6.45 < 6.50 < 6.54 Hence, the given decimals can be arranged in the ascending order as follows: 6.05, 6.40, 6.45, 6.50 and 6.54
(iv) 3.3, 3.303, 3.033, 0.33, 3.003
8. Arrange the following decimals in an descending order:
(i) 7.3, 8.73, 73.03, 7.33, 8.073
(ii) 3.3, 3.03, 30.3, 30.03, 3.003
(iii) 2.7, 7.2, 2.27, 2.72, 2.02, 2.007
(iv) 8.88, 8.088, 88.8, 88.08, 8.008
Solution:
(ii) 3.3, 3.03, 30.3, 30.03, 3.003
(iv) 8.88, 8.088, 88.8, 88.08, 8.008
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