Compare & order decimals
Theory
To compare decimals, line them up by place value and compare the tenths first, then the hundredths, and so on. More digits does not mean a larger number, and a zero on the end adds no value: \(0.5 = 0.50\).
To compare decimals is to decide which is larger; to order them is to line them up from smallest to largest or the other way.
Start at the tenths. The larger tenths digit makes the larger decimal. If the tenths are equal, move right to the hundredths, then the thousandths.
A trailing zero adds no value, so \(0.5 = 0.50\); compare place by place, not by counting digits.
Work from the largest place to the smallest, stopping as soon as the digits differ.
| Pair | Compare | Result |
|---|---|---|
| \(0.7,\ 0.68\) | tenths \(7 > 6\) | \(0.7 > 0.68\) |
| \(0.45,\ 0.405\) | hundredths \(5 > 0\) | \(0.45 > 0.405\) |
| \(0.250,\ 0.25\) | equal | \(0.250 = 0.25\) |
How to compare two decimals
- Line up the numbers by place value under the decimal point.
- Compare the tenths. The larger tenths digit wins.
- If equal, move to the hundredths, then thousandths, until the digits differ.
Compare the tenths first: \(7 > 6\).
| \(0.7\) | \(=\) | \(0.68 \text{ (larger)}\) |
A zero on the end adds no value.
| \(0.170\) | \(=\) | \(0.17\) |
Compare tenths, then split ties by the hundredths.
| \(\text{order}\) | \(=\) | \(0.054,\ 0.405,\ 0.45,\ 0.5\) |
Fastest is the smallest time; compare the tenths.
| \(\text{fastest}\) | \(=\) | \(12.045\text{ s}\) |
Common pitfalls
Frequently asked questions
How do you compare two decimals?
Line them up by place value and compare the tenths first. If the tenths are equal, compare the hundredths, then the thousandths.
Is a decimal with more digits always larger?
No. \(0.125\) has more digits than \(0.5\) but is smaller, because its tenths digit \(1\) is less than \(5\).
Does a zero on the end change a decimal?
No. \(0.250\) is the same as \(0.25\); a trailing zero adds no value.
What does ascending order mean?
Ascending order means smallest first. Descending order means largest first.