Chapter 5: Decimal Fractions — Exercise 5(B) | Solutions for Class 6 RS Aggarwal ICSE Foundation Mathematics

Exercise 5(B)

Question 1

Convert each of the sets of unlike decimals into like decimals:

(i) 9.4, 65.83, 0.065

(ii) 0.5, 7.573, 4.26, 8.4

(iii) 1.2, 0.06, 3.5, 6.38

(iv) 2.8, 16.85, 64.056, 143.625

Answer

(i) Maximum number of decimal places in the given numbers is 3. So, we can convert each of the decimals into one having 3 decimal places by annexing zeros.

9.4 = 9.400

65.83 = 65.830

0.065 = 0.065

As 9.400, 65.830, 0.065 have equal number of decimal places, they are like decimals.

(ii) Maximum number of decimal places in the given numbers is 3. So, we can convert each of the decimals into one having 3 decimal places by annexing zeros.

0.5 = 0.500

7.573 = 7.573

4.26 = 4.260

8.4 = 8.400

As 0.500, 7.573, 4.260, 8.400 have equal number of decimal places, they are like decimals.

(iii) Maximum number of decimal places in the given numbers is 2. So, we can convert each of the decimals into one having 2 decimal places by annexing zeros.

1.2 = 1.20

0.06 = 0.06

3.5 = 3.50

6.38 = 6.38

As 1.20, 0.06, 3.50, 6.38 have equal number of decimal places, they are like decimals.

(iv) Maximum number of decimal places in the given numbers is 3. So, we can convert each of the decimals into one having 3 decimal places by annexing zeros.

2.8 = 2.800

16.85 = 16.850

64.056 = 64.056

143.625 = 143.625

As 2.800, 16.850, 64.056, 143.625 have equal number of decimal places, they are like decimals.

Question 2

Fill in the placeholders with > or <:

(i) 63.4 ${\boxed{\phantom{63}}}$ 36.85

(ii) 4.805 ${\boxed{\phantom{63}}}$ 4.85

(iii) 8.23 ${\boxed{\phantom{63}}}$ 8.32

(iv) 5.06 ${\boxed{\phantom{63}}}$ 5.006

(v) 7.86 ${\boxed{\phantom{63}}}$ 7.806

(vi) 0.98 ${\boxed{\phantom{63}}}$ 1

Answer

(i) The given decimals are 63.4 and 36.85. Comparing their whole number parts clearly shows that, 63 > 36.

Therefore, 63.4 > 36.85.

(ii) The given decimals are 4.805 and 4.85.

Writing them as like decimals: 4.805 and 4.850.

Comparing the decimal parts, we find that 805 < 850.

Therefore, 4.805 < 4.85.

(iii) The given decimals are 8.23 and 8.32. Their whole number parts are equal. Comparing their tenths digits, 2 < 3.

Therefore, 8.23 < 8.32.

(iv) The given decimals are 5.06 and 5.006.

Writing them as like decimals: 5.060 and 5.006.

Comparing the decimal parts, 60 > 6.

Therefore, 5.06 > 5.006.

(v) The given decimals are 7.86 and 7.806.

Writing them as like decimals: 7.860 and 7.806.

Comparing the decimal parts, 860 > 806.

Therefore, 7.86 > 7.806.

(vi) The given decimals are 0.98 and 1.

Comparing their whole number parts, 0 < 1.

Therefore, 0.98 < 1.

Question 3

Arrange the following decimals in ascending order:

(i) 3.6, 4.2, 3.57, 4.18, 3.06, 4.08

(ii) 5.37, 3.57, 3.5, 5.3, 5.7, 3.07

(iii) 0.7, 0.007, 0.07, 7.7, 7.07, 0.77

(iv) 2.2, 2.02, 0.22, 0.02, 0.202, 2.002

(v) 76.8, 68.7, 86.7, 87.6, 78.6, 7.86

Answer

(i) The maximum number of decimal places in the given decimals is 2. So, we convert each of the given decimals into like decimals having two decimal places by annexing zeros.

The decimals are: 3.60, 4.20, 3.57, 4.18, 3.06, 4.08

Clearly, 3.06 < 3.57 < 3.60 < 4.08 < 4.18 < 4.20.

Hence, the given decimals in ascending order are:

3.06 < 3.57 < 3.6 < 4.08 < 4.18 < 4.2.

(ii) The maximum number of decimal places in the given decimals is 2. So, we convert each of the given decimals into like decimals having two decimal places by annexing zeros.

The decimals are: 5.37, 3.57, 3.50, 5.30, 5.70, 3.07

Clearly, 3.07 < 3.50 < 3.57 < 5.30 < 5.37 < 5.70.

Hence, the given decimals in ascending order are:

3.07 < 3.5 < 3.57 < 5.3 < 5.37 < 5.7.

(iii) The maximum number of decimal places in the given decimals is 3. So, we convert each of the given decimals into like decimals having three decimal places by annexing zeros.

The decimals are: 0.700, 0.007, 0.070, 7.700, 7.070, 0.770

Clearly, 0.007 < 0.070 < 0.700 < 0.770 < 7.070 < 7.700.

Hence, the given decimals in ascending order are:

0.007 < 0.07 < 0.7 < 0.77 < 7.07 < 7.7

(iv) The maximum number of decimal places in the given decimals is 3. So, we convert each of the given decimals into like decimals having three decimal places by annexing zeros.

The decimals are: 2.200, 2.020, 0.220, 0.020, 0.202, 2.002

Clearly, 0.020 < 0.202 < 0.220 < 2.002 < 2.020 < 2.200.

Hence, the given decimals in ascending order are:

0.02 < 0.202 < 0.22 < 2.002 < 2.02 < 2.2

(v) The maximum number of decimal places in the given decimals is 2. So, we convert each of the given decimals into like decimals having two decimal places by annexing zeros.

The decimals are: 76.80, 68.70, 86.70, 87.60, 78.60, 7.86

Clearly, 7.86 < 68.70 < 76.80 < 78.60 < 86.70 < 87.60.

Hence, the given decimals in ascending order are:

7.86 < 68.7 < 76.8 < 78.6 < 86.7 < 87.6

Question 4

Arrange the following decimals in descending order:

(i) 6.6, 0.06, 0.6, 0.006, 6.66

(ii) 3.3, 3.03, 0.33, 33.3, 0.303, 30.3

(iii) 2.9, 3.6, 9.2, 6.3, 3.06, 6.03

(iv) 77.7, 0.7, 7.7, 0.07, 7.07, 7.77

(v) 7.35, 3.75, 5.3, 3.57, 5.37, 5.75

Answer

(i) The maximum number of decimal places in the given decimals is 3. So, we convert each of the given decimals into like decimals having three decimal places by annexing zeros.

The decimals are: 6.600, 0.060, 0.600, 0.006, 6.660

Clearly, 6.660 > 6.600 > 0.600 > 0.060 > 0.006.