RS Aggarwal class 6 solutions chapter 7 decimals is provided here. Solving questions from RS Aggarwal for class 6 will help students to practice a variety of questions from basic to advanced level. Sometimes the questions from RS Aggarwal are also asked in school examinations. In this chapter, the students will learn how to represent decimals on a number line, comparing decimals and lot more.

**1. Write each of the following in figures:**

**(i) Fifty-eight point six three**

Ans â€“ 58.63

**(ii) One hundred twenty-four point four two five**

Ans â€“ 124.425

**(iii) Seven point seven six**

Ans – 7.76

**(iv) Nineteen point eight**

Ans â€“ 19.8

**(v) Four hundred four point zero four four**

Ans â€“ 404.044

**(vi) Point one seven three**

Ans â€“ 0.173

**(vii) Point zero one five**

Ans â€“ 0.015

**2. Write the place value of each digit in each of the following decimals:****(i) 14.83 **

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 = 8/10

Place value of 3 = 3 hundredth = 3/100

**(ii) 275.269**

In 275.269, we have:

Place value of 2 = 2 hundredth = 200

Place value of 7 = 1 tens = 70

Place value of 5 = 5 ones = 5

Place value of 2 = 2 tenth = 2/10

Place value of 6 = 6 hundredth = 6/100

Place value of 9 = 9 thousandth = 9/1000

**(iii) 46.075**

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 = 0/10 = 0

Place value of 7 = 7 hundredths = 7/100

Place value of 5 = 5 thousandths = 5/1000

**(iv) 302.459**

In 302.459, we have:

Place value of 3 = 3 hundredths = 300

Place value of 0 = 0 tens = 0

Place value of 2 = 2 ones = 2

Place value of 4 = 4 tenths = 4/10

Place value of 5 = 5 hundredths = 5/100

Place value of 9 = 9 thousandths = 9/1000

**(v) 5370.34**

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 = 3/10

Place value of 4 = 4 hundredths = 4/100

**(vi) 186.209**

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 = 2/10

Place value of 0 = 0 hundredths = 0

Place value of 9 = 9 thousandths = 9/1000

**3. Write each of the following decimals in expanded form:**

**(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 + 5thousandths

= \( 20 + 4 + \frac {6} {10} + \frac {7} {100} + \frac {5} {1000} \)

**(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) \( 40 + 6 + \frac {7} {10} + \frac {9} {100} \)**

= 46 + 0.7 + 0.9 = 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**

Each of the numbers has maximum 3 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.

7.5 = 7.500

64.23 = 64.230

0.074 = 0.074

**(ii) 0.6, 5.937, 2.36, 4.2**

Each of the numbers has maximum 3 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.

0.6 = 0.600

5.937 = 5.937

2.36 = 2.360

4.2 = 4.200

**(iii) 1.6, 0.07, 3.58, 2.9**

Each of the numbers has maximum 2 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.

1.6 = 1.60

0.07 = 0.07

3.58 = 3.58

2.9 = 2.90

**(iv) 2.5, 0.63, 14.08, 1.637**

Each of the numbers has maximum 3 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.

2.5 = 2.500

0.63 = 0.630

14.08 = 14.080

1.637 = 1.637

**6. Fill each of the following blanks with 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**

**Answer:**

(i) 84.23_>__76.35

Since 84 is greater than 76, 84.23 is greater than 76.35. (Comparing the whole number parts)

(ii) 7.608__<__7.68

Since 8 is greater than 0 at the hundredths place, 7.608 is smaller than 7.608.

(iii) 8.34__<___8.43

Since 4 is greater than 3 at the tenths place, 8.34 is smaller than 8.43.

(iv)12.06_>__12.006

Since 6 is greater than 0 at the hundredths place, 12.06 is greater than 12.006.

(v) 3.85__>__3.805

Since 5 is greater than 0 at the hundredths place, 3.850 is greater than 3.805.

(vi) 0.97__<__1.07

Since 1 is greater than 0, 0.97 is smaller than 1.07. (Comparing the whole number parts)

**7. Arrange the following decimals in ascending order:**

**(i) 5.8, 7.2, 5.69, 7.14, 5.06**

Converting the given decimals into like decimals:

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, 5.80, 7.14 and 7.2

**(ii) 0.6, 6.6, 6.06, 66.6, 0.06**

Converting the given decimals into like decimals:

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**

Converting the given decimals into like decimals:

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**

Converting the given decimals into like decimals:

3.300, 3.303, 3.033, 0.330, 3.003

Clearly, 0.330 < 3.003 < 3.033 < 3.300 < 3.303

Hence, the given decimals can be arranged in the ascending order as follows:

0.330, 3.003, 3.033, 3.300 and 3.303.

**8. Arrange the following decimals in descending order:**

**(i) 7.3, 8.73, 73.03, 7.33, 8.073**

Converting the given decimals into like decimals:

7.300, 8.730, 73.030**, **7.330, 8.073

Clearly, 73.030 > 8.730 > 8.073 > 7.330 > 7.300

Hence, the given decimals can be arranged in the descending order as follows:

73.03, 8.73, 8.073, 7.33 and 7.3.

**(ii) 3.3, 3.03, 30.3, 30.03, 3.003**

Converting the given decimals into like decimals:

3.300, 3.030, 30.3000, 30.030, 3.003

Clearly, 30.300 > 30.030 > 3.300 > 3.030 > 3.003

Hence, the given decimals can be arranged in the descending order as follows:

30.3, 30.03, 3.3, 3.03 and 3.003.

**(iii) 2.7, 7.2, 2.27, 2.72, 2.02, 2.007**

Converting the given decimals into like decimals:

2.700, 7.200, 2.270, 2.720, 2.020, 2.007

Clearly, 7.200 > 2.720 > 2.700 > 2.270 > 2.020 > 2.007

Hence, the given decimals can be arranged in the descending order as follows:

7.2, 2.72, 2.7, 2.27, 2.02 and 2.007

**(iv) 8.88, 8.088, 88.8, 88.08, 8.008**

Converting the given decimals into like decimals:

8.880, 8.088, 88.800, 88.080, 8.008

Clearly, 88.800 > 88.080 > 8.880 > 8.088 > 8.008

Hence, the given decimals can be arranged in the descending order as follows:

88.8 , 88.08, 8.88, 8.088 and 8.008.