RS Aggarwal Class 6 Solutions Decimals

1. Write each of the following in figures:

(i) Fifty-eight point six three

Ans – 58.63

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

Ans – 124.425

(iii) Seven point seven six

Ans – 7.76

(iv) Nineteen point eight

Ans – 19.8

(v) Four hundred four point zero four four

Ans – 404.044

(vi) Point one seven three

Ans – 0.173

(vii) Point zero one five

Ans – 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.


Practise This Question

Statement I : Factories should have tall chimneys.

Statement II: Tall chimneys in factories help in releasing harmful smoke high in the atmosphere.