To know the order relation in decimals is relatively easier compared to that in vulgar Fractions.

There, we have to find the L.C.M. of the denominators of the given set of fractions and convert them into equivalent fractions using that L.C.M. to compare.

Here the following Note is made use of. Note :

putting any number of zeroes to the extreme right side of the decimal part of a decimal does not change the value of the decimal.

Method of Comparing decimals

Step 1 : First compare the whole number parts. The decimal with greater whole number is greater.

Step 2 : Make the number of digits after the decimal point equal by putting zeroes to the extreme right side of the decimal part, if required.

Step 3 : If the whole number parts are equal, compare the tenths digits. The decimal with the bigger digit in the tenths place is greater.

Step 4 : If the tenths digits are equal, compare the hundredths digits, and so on.

Example 1 of Comparing decimals

Compare 51.42 and 49.79

Solution: The given decimals are 51.42 and 49.79. First, let us compare the whole number parts. Obviously, 51 > 49. ∴ 51.42 > 49.79. Ans.

Example 2 of Comparing decimals

Compare 83.8 and 83.59

Solution: here, the whole number part of the given decimals is same.

The given decimals are 83.8 and 83.59 or 83.80 and 83.59.

Write the following decimals in ascending order. 16.01, 7.23, 0.9, 0.965, 1.001.

Solution: Here, the whole numbers are 16, 7, 0, 0, 1. In ascending order they are 0, 0, 1, 7, 16. The two decimals with whole number part 0, are 0.9 and 0.965 or 0.900 and 0.965. Here, the digits in the tenths place are equal. The digits in the hundredths place are 0 and 6. Obviously, 0 < 6. ∴0.900 < 0.965.

Hence, the given decimals in ascending order are 0.9, 0.965, 1.001, 7.23, 16.01. Ans.

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Write the following decimals in descending order. 99.9, 0.9, 9.9, 0.09, 9.09. 9.99

Solution: Here, the whole numbers are 99, 0, 9 In descending order they are 99, 9, 0. So, the decimal with 99 as whole number is the largest, followed by those with whole number 9 and then with 0.

The decimals with 9 as whole number are 9.9, 9.09, 9.99 or 9.90, 9.09, 9.99 Comparing tenths' digits, 9.09 is less than the other two as 0 < 9. Comparing hundredths' digits, 9.99 > 9.90 as 9 > 0. Thus, 9.99 > 9.90 > 9.09.

The decimals with 0 as whole number are 0.9, 0.09 or 0.90, 0.09 Comparing tenths' digits, 0.90 > 0.09, as 9 > 0.

Hence, the given decimals in descending order are 99.9 > 9.99 > 9.90 > 9.09 > 0.90 > 0.09. Ans.

Exercise on comparing decimals

Fill in the blank with > or <

17.93 --- 16.99

1.708 --- 1.78

34.78 --- 34.87

3.09 --- 3.009

.99 --- 1

Arrange the following decimals in ascending order :

1.6, 2.2, 1.57, 2.18, 1.18, 2.08

0.8, 0.008, 0.08, 8.8, 8.08, 0.88

Arrange the following decimals in descending order :

3.3, 0.03, 0.3, 0.003, 3.33, 33.3

4.9, 5.6, 9.2, 8.3, 5.06, 8.03

For Answers see at the bottom of the page.

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