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0.724 is larger than 0.7231, so in ordering them from smaller to larger 0.7231 comes first, that is in order smaller to larger, they are: 0.7231, 0.724.
When comparing decimals, look at the digits in pairs starting with the digits just to the right of the decimal point and going right:
If a pair of digits are equal, then try the next pair to the right, otherwise whichever decimal contains the larger digit is the larger decimal.
If one decimal runs out of digits when the other decimal hasn't, then the one which has run out of digits is the smaller decimal.
Comparing 0.724 with 0.7231
1st pair: 7 (from 0.724) & 7 (from 0.7231) - equal, try the next pair
2nd pair: 2 (from 0.724) & 2 (from 0.7231) - equal try the next pair
3rd pair: 4 (from 0.724) & 3 (from 0.7231) - 4 is larger, thus 0.724 is larger than 0.7231.
Note that trailing zeros after a decimal point (that is any zero that is not followed by a non-zero digit) can be removed from a decimal without changing its value.
Similarly, zeros can be appended (added to the end) of a decimal number after the decimal point without changing its value.
So it may be easier when comparing decimals to make them all the same length by appending zeros to the shorter ones.
With 0.724 and 0.7231:
- 0.724 is 3 digits long
- 0.7231 is 4 digits long
So appending a single zero to 0.724:
- 0.724 with a zero appended is 0.7240
makes them both the same length (4 digits long).
Now the comparison can be made until one digit is larger than the other (giving the larger decimal) or the both run out of digits, in which case the two decimals are equal.
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∙ 12y ago
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