Comparing and ordering decimals

To compare two decimals, line up their decimal points and compare one place at a time, starting from the left. The first place where they differ decides the comparison, and nothing further to the right can overturn it.

The method

1. Write the numbers with their decimal points aligned.
2. Pad the shorter one with zeros on the right so both have the same number of decimal places. This changes nothing, because a trailing zero adds no value.
3. Compare the whole number parts. If they differ, you are done.
4. Otherwise compare tenths, then hundredths, then thousandths, stopping at the first difference.

Ordering a list

Once every number has three decimal places, the comparison is exactly the same as ordering the whole numbers 70, 700, 707, 770.

On a number line

Between 0 and 1 there are ten tenths, and between any two tenths there are ten hundredths. Placing 0.47 means going almost half way, and placing 0.5 means going exactly half way. Drawing it once settles the question for most students better than any rule.

Where this matters

Comparing decimals is one of the few school skills that gets used almost daily as an adult.

• Prices. Which unit price is lower, 2.4 or 2.35 per kilogram.
• Times. A race won by 10.09 against 10.1 is decided in the hundredths place.
• Measurements. Deciding whether a shelf of 1.2 metres fits an alcove of 1.18 metres, where guessing costs a return trip to the shop.

In each case padding to the same number of decimal places settles the question immediately: 2.40 against 2.35, 10.09 against 10.10, 1.20 against 1.18.

Common mistakes

Longer means larger

The single most common decimal error. 0.4 is greater than 0.399, because four tenths beats three tenths whatever follows.

Comparing without aligning

Writing the numbers ragged and comparing the first digits you see leads to comparing tenths against hundredths. Align the points before anything else.

Check yourself