Exercise 1.3 (Comparison of Decimals)

Exercise 1.3

1. Compare the following decimal numbers and find out the smaller number.

(i) 2.08, 2.086

(ii) 0.99, 1.9

(iii) 3.53, 3.35

(iv) 5.05, 5.50

 (v) 123.5, 12.35

(i) 2.08, 2.086

208 = 2 + 0 × 1/10 + 8 × (1/100) + 0 × 1/1000

2086 = 2 + 0 × 1/10 + 8 × (1/100) + 6 ⊂ (1/1000)

In this case, the two numbers have same digits upto hundredths place. But the thousandth place of 2.086 is 6, which is greater than 0, which is the thousandth place of 2.08.

So, 2.08 < 2.086

The smaller number is 2.08.

(ii) 0.99, 1.9

0.99 = 0 + 9/10  +  9/100

19 = 1 + 9/10

The whole number 1 is greater than 0.

So, 0.99 < 1.9

The smaller number is 0.99.

(iii) 3.53,3.35

3.53 = 3 + 5/10 + 3/ 100

3.35 = 3 + 3/10 + 5/100

Here, the whole number parts of the given two numbers are equal. Comparing the digits at tenths place, we get

5 > 3

So, 3.53 > 3.35

The smaller number is 3.35.

(iv) 5.05,5.50

5.05 = 5 +  0/10  + 5/100

5.50 = 5 + 5/10 + 0/100

Here, the whole number parts of the given two numbers are equal. Comparing the digits at tenths place,

Weget 0 < 5       So, 5.05 < 5.50

The smaller number is 5.05. 

(v) 123.5, 12.35

1235 = 100 – 20 + 3 + 5/10

1235 = 10 + 2 + 3/10 + 5/100

Here, In the whole number parts of the given two numbers

123 > 12.

So, 123.5 > 12.35

The smaller number is 12.35.

2. Arrange the following in ascending order.

(i) 2.35, 2.53, 5.32, 3.52, 3.25

(ii) 123.45, 123.54, 125.43, 125.34, 125.3

 (i) 2.35, 2.53, 5.32, 3.52, 3.25

Comparing the whole number parts, 2 < 3 < 5

In 2.35 and 2.53

235 = 2 + 3/10 + 5/100

Comparing the tenths place, 3 < 5

So, 2.35 < 2.53

In 3.52 and 3.25

3.52 = 3 + 5/10 + 2/100

3.25 = 3+ 2/10 + 5/100

Comparing the tenths place, 2 < 5

So, 3.25 < 3.52

So, Ascending order is 2.35, 2.53, 3.25, 3.52, 5.32.

(ii) 123.45, 123.54, 125.43, 125.34, 125.3

Comparing the whole numbers, 123 < 125

In 123.45 and 123.54, The whole number parts are equal. Comparing the tenths place, 4 < 5

So, 123.45 < 123.54

In 125.43, 125.34 and 125.3, The whole number parts are equal. Comparing the tenths place, 3 < 4. 

In 125.34 and 125.3, the tenths place ofthe two numbers are equal.

So comparing the hundredths place 0< 4,

So, 125.3 < 125.34

So,Ascending order is 123.4, 123.54, 125.3, 125.34, 125.43.

3. Compare the following decimal numbers and find the greater number.

(i) 24.5, 20.32

(ii) 6.95, 6.59

(iii) 17.3, 17.8

(iv) 235.42, 235.48

(v) 0.007, 0.07

(vi) 4.571, 4.578

(i) 24.5, 20.32

Compare the whole number parts, 24 > 20

So, 24.5 > 20.32

The greater number is 24.5.

(ii) 6.95, 6.59

The whole number parts of the two given numbers are equal.

So, Comparing the tenth place , 9 > 5

So, 6.95 > 6.59

The greater number is 6.95.

(iii) 17.3, 17.8

The whole number parts of the given two numbers are equal.

So, Comparing tenth place, 3 < 8

So, 17.3 < 17.8

The greater number is 17.8.

(iv) 235.42, 235.48

The whole number parts and the tenth places of the two numbers are equal.

So, Comparing hundred place, 2 < 8

So, 235.42 < 235.48

The greater number is 235.48.

(v) 0.007, 0.07

The whole number parts and the tenth places of the two numbers are equal.

So, Comparing hundredth place, 0 < 7

So, 0.007 < 0.07

The greater number is 0.07. 

(vi) 4.571, 4.578

The two numbers have same digits upto hundredth place.

 So, Comparing thousandth place, 1 < 8

So, 4.571 < 4.578

The greater number is 4.578.

4. Arrange the given decimal numbers in descending order.

(i) 17.35, 71.53, 51.73, 73.51, 37.51

(ii) 456.73, 546.37, 563.47, 745.63, 457.71

(i) 17.35, 71.53, 51.73, 73.51, 37.51

In whole number part,

73 > 71 > 51 > 37 > 17

So,

73.51 > 71.53 > 51.73 > 37.51 > 17.35

The descending order,

73.51, 71.53, 51.73, 37.51, 17.35

(ii) 456.73, 546.37, 563.47, 745.63, 457.71

In whole number part,

745 > 563 > 546 > 457 > 456

So,

745.63 > 563.47 > 546.37 > 457.71 > 456.73

The descending order

745.63, 563.47, 546.37, 457.71, 456.73

Objective type questions

5. 0.009 is equal to

(i) 0.90

(ii) 0.090

(iii) 0.00900

(iv) 0.900

Answer : (iii) 0.00900

6. 37.70 ___ 37.7

(i) =

(ii) <

(iii) >

(iv) ≠

Answer : (i) =

7. 78.56 ___ 78.57

(i) <

(ii) >

(iii) =

(iv) ≠

Answer : (i)  <

ANSWERS:

Exercise 1.3

1. (i) 2.08 (ii) 0.99 (iii) 3.35 (iv) 5.05 (v) 12.35

2. (i) 2.35, 2.53, 3.25, 3.52, 5.32 (ii) 123.45, 123.54, 125.3, 125.34, 125.43

3. (i) 24.5 (ii) 6.95 (iii) 17.8 (iv) 235.48  (v) 0.07 (vi) 4.578

4. (i) 73.51, 71.53, 51.73, 37.51, 17.35 (ii) 745.63, 563.47, 546.37, 457.71, 456.73

Objective type questions

5. (iii) 0.00900

6. (i) =

7.(i) <