# Comparison of Decimal Fractions

We will discuss here about the comparison of decimal fractions.

While comparing natural numbers we first compare total number of digits in both the numbers and if they are equal then we compare the digit at the extreme left. If they also equal then we compare the next digit and so on. We follow the same pattern while comparing the decimals.

We know that a decimal number has whole part and a decimal part. The decimal number with the greater whole part is greater.

For example, 5.4 is greater than 3.98.

If the whole parts are equal, first convert the given decimals into like decimals and then compare. We compare the digits in the tenths place. The decimal number with the greater digit in the tenths place is greater.

For example, 9.85 is greater than 9.65.

If the digits in the tenths place are equal, compare the digits in the hundredths place. The decimal number with the greater digit in the hundredths place is greater.

For example, 0.58 > 0.55.

If the digits in the tenths and the hundredths place are same, the decimal number with the greater digit in the thousandths place is greater. For example, 51.268 > 51.265

Examples on Comparing Decimals:

1. Compare 0.6 and 0.8.

Solution:

0.6 = 6 tenths

0.8 = 8 tenths

Because 8 tenths > 6 tenths

Thus, 0.8 > 0.6

2. Compare 0.317 and 0.341

Solution:

0.317     = 0.3 + 0.01 + 0.007

= 3 tenths + 1 hundredths + 7 thousandths

0.341     = 0.3 + 0.04 + 0.001

= 3 tenths +4 hundredths + 1 thousandths

Because 3 tenths = 3 tenths,

Now, compare next digit

1 hundredths < 4 hundredths

Thus, 0.317 < 0.341

Steps of Comparison of Decimal Fractions are given below:

Step I: First we need to observe the integral part.

For example:

(i) 104 < 140, this is how we check the integral part

(ii) 153 = 153

(iii) 112 > 121

Step II: When the integral part is same then compare the tenths place

For example:

(i) 1.4 < 1.9,

(ii) 1.5 = 1.50

(iii) 16.2 > 16.1

Step III: When the tenth place is same compare the hundredths place.

For example:

(i) 10.04 < 10.09,

(ii) 1.97 = 1.97

(iii) 71.92 > 71.90

In this way we first check the integral part and then move to the decimal places one by one.

For example:

1. Which is greater, 12.0193 or 102.01?

Solution:

First check the integer part

12 and 102

12 is < 102

102.01 is greater.

2. Which is smaller, 19.023 or 19.027?

Solution:

For each of these decimals the integral part is the same. So compare the tenths place. This is also same, check the hundredths places that is also same then move to the next decimal place.

Therefore, 19.023 < 19.027

So, 19.023 is smaller.

3. Find the greater number; 162.19 or 126.91.

Solution:

162.19 is greater than 126.91.

4. Which number is greater 293.82 or 293.62?

Solution:

First check the integer part,

293 = 293

Then the tenth place

8 > 6

Now the hundredth place

2 = 2

Therefore, 293.82 is greater than 293.62.

5. Find the greater number; 1432.97 or 1432.99

Solution:

First check the integer part,

1432 = 1432

Then the tenth place

9 = 9

Now the hundredth place

7 < 9

Therefore, 1432.99 is greater than 1432.97

6. Which number is greater 187.653 or 187.651?

Solution:

First check the integer part,

187 = 187

Then the tenth place

6 = 6

Then the hundredth place

5 = 5

Now the thousandth place

3 > 1

Therefore, 187.653 is greater than 187.651

7. Which number is greater 153.017 or 153.017?

Solution:

First check the integer part,

153 = 153

Then the tenth place

0 = 0

Then the hundredth place

1 = 1

Now the thousandth place

7 = 7

Therefore, 153.017 = 153.017

8. Find the greater number; 1324.42 or 1324.44

Solution:

First check the integer part,

1324 = 1324

Then the tenth place

4 = 4

Now the hundredth place

2 < 4

Therefore, 1324.44 is greater than 1324.42

9. Which number is greater 804.07 or 804.007?

Solution:

First check the integer part,

804 = 804

Then the tenth place

0 = 0

Then the hundredth place

7 > 0

Therefore, 804.07 is greater than 804.007

10. Find the greater number; 211.21 or 211.21

Solution:

First check the integer part,

211 = 211

Then the tenth place

2 = 2

Now the hundredth place

1 = 1

Therefore, 211.21 = 211.21

11. Write in ascending order using < sign:

(a) 43.81, 43.18, 43.08, 43.80

Solution:

43.08 < 43.18 < 43.80 < 43.81

(b) 89.09, 89.90, 89.01, 89.03

Solution:

89.01 < 89.03 < 89.09 < 89.90

(c) 53.35, 53.53, 53.30, 53.05

Solution:

53.05 < 53.30 < 53.35 < 53.53

(d) 61.16, 61.61, 61.06, 61.36

Solution:

61.06 < 61.16 < 61.36 < 61.61

12. Arrange the following decimal numbers in ascending order.

9.02; 2.56; 2.66; 8.02

Solution:

The greatest integral part is 9. So, 9.02 is the greatest number in the above set. 2.56 and 2.66 have equal integral parts, we compare the digits in the tenths place 5 > 6. So, 2.66 > 2.56.

The decimal numbers in ascending order are 2.56; 2.66; 8.02; 9.02

13. Compare and put the appropriate sign:

(i) 13.6 ______ 1.36

(ii) 65.010 ______ 65.110

(iii) 209.008 ______ 210.007

(iv) 47.981 ______ 29.999

(i) >

(ii) <

(iii) <

(iv) >

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