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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