Ordering Decimals

Ordering decimals is referred to as comparing decimals. We will compare the decimals by first changing them into like fractions. We will first count the maximum number of places after the decimal point and accordingly put zeros which comprises of less number of places after the decimal point. After changing it into like fractions we will compare the decimals like we compare whole numbers ignoring the decimal.

For Example:

Compare: 45.235 and 45.3256

Change into like fractions:

45.2350 and 45.3256

If we ignore the decimal then:

45.3256 > 45.2350

This is how we will order the decimal numbers. The decimals could be ordered in ascending or descending order as mentioned in the sums.

Here are few examples on ordering of decimals.

Arrange the following decimals in ascending order after changing them into like fractions:

(i) 12.321, 12.021, 12.0569, 12.0453, 12.001, 12.01, 12.004

Changing decimals into like decimal fractions

12.3210, 12.0210, 12.0569, 12.0453, 12.0010, 12.0100, 12.0040

Since now all the numbers have the same whole number we will have to check the decimal part by ignoring the decimal point.

3210, 0210, 0569, 0453, 0010, 0100, 0040

0010 < 0040 < 0100 < 0210 < 0453 < 0569 < 3210

When arranged in ascending order:

12.0010 < 12.0040 < 12.0100 < 12.0210 < 12.0453 < 12.0569 < 12.3210 

(ii) 50.32, 50.326, 50.280, 50.960, 50.3214, 50.7520, 50.364

Changing decimals into like decimal fractions

50.3200, 50.3260, 50.2800, 50.9600, 50.3214, 50.7520, 50.3640

Since now all the numbers have the same whole number we will have to check the decimal part by ignoring the decimal point.

3200, 3260, 2800, 9600, 3214, 7520, 3640

2800 < 3200 < 3214 < 3260 < 7520 < 9600

When arranged in ascending order:

50.2800 < 50.3200 < 50.3214 < 50.3260 < 50.7520 < 50.9600

(iii) 75.452, 75.436, 75.94, 75.365, 75.412, 75.978, 75.001

Changing decimals into like decimal fractions

75.452, 75.436, 75.940, 75.365, 75.412, 75.978, 75.001

Since now all the numbers have the same whole number we will have to check the decimal part by ignoring the decimal point.

452, 436, 940, 365, 412, 978, 001

001 < 365 < 412 < 436 < 452 < 940 < 978

When arranged in ascending order:

75.001 < 75.365 < 75.412 < 75.436 < 75.452 < 75.940 < 75.978

Arrange the following decimals in descending order after changing them into like fractions:

(i) 115.32, 115.0023, 115.674, 115.3030, 115.0420, 115.500

Changing decimals into like decimal fractions

115.3200, 115.0023, 115.6740, 115.3030, 115.0420, 115.5000

Since now all the numbers have the same whole number we will have to check the decimal part by ignoring the decimal point.

3200, 0023, 6740, 3030, 0420, 5000

6740 > 5000 > 3200 > 3030 > 0420 > 0023

When arranged in descending order:

115.6740 > 115.5000 > 115.3200 > 115.3030 > 115.0420 > 115.0023

(ii) 120.325, 53.4, 5.065, 95.4, 75.003, 41.0023, 68.3214

Changing decimals into like decimal fractions

120.3250, 53.4000, 5.0650, 95.4000, 75.0030, 41.0023, 68.3214

Since now all the numbers have different whole numbers we will have to check the whole number part

120 > 95 > 75 > 68 > 53 > 41 > 5

When arranged in descending order:

120.3250 > 95.4000 > 75.0030 > 6.3214 > 53.4000 > 41.0023 > 5.0650

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