Compare & order decimals
Theory
Comparing and ordering decimals to two decimal places is a Year 4 maths skill: line up the decimal points and check each place in turn, tenths first, then hundredths. This page shows how a place value chart and a number line make it clear that a longer decimal is not always bigger, and how equivalent decimals like \(0.4 = 0.40\) help you compare. Comparing decimals starts in Year 4; in the Australian Curriculum, ordering decimals is Year 5 content. Curriculum: VC2M4N01 / AC9M4N01 (ordering: AC9M5N01).
A decimal is a number with a decimal point. The digits after the point show parts of a whole: the first place is tenths and the second place is hundredths. In \(0.26\) the 2 means 2 tenths and the 6 means 6 hundredths.
To compare decimals means to say which is larger or smaller, using the symbols \(<\), \(>\) or \(=\). To order decimals means to sort a list from smallest to largest, or from largest to smallest.
Equivalent decimals have the same value but look different. A zero on the end does not change the value, so \(0.4 = 0.40\) and \(0.8 = 0.80\). Giving both numbers the same number of decimal places makes them easy to line up and compare.
Decimals do not need formulas, but these place value facts make comparing and ordering quick.
How to compare or order decimals
- Give them the same places. Add a zero on the end where needed so both decimals have the same number of decimal places, so \(0.7\) becomes \(0.70\).
- Compare from the left. Check the ones, then the tenths, then the hundredths. Stop at the first place where the digits are different.
- Decide or order. The larger digit in that place means the larger number. To order a list, compare two at a time and sort from smallest to largest.
Decimals with wholes. Compare the ones first: \(2.9 < 3.1\) because \(2\) ones is less than \(3\) ones. If the ones are the same, move to the tenths: \(4.62 > 4.6\) because \(4.60\) has \(0\) hundredths.
Making the largest or smallest decimal. To make the largest number from some digits, put the biggest digit in the biggest place. With \(1\), \(4\) and \(7\) in the form \(\square.\square\square\), the largest is \(7.41\) and the smallest is \(1.47\).
| \(0.7\) | \(=\) | \(0.70\) |
| \(\text{tenths}\) | \(:\) | \(7 > 4\) |
| \(0.70\) | \(>\) | \(0.49\) |
Even though \(0.49\) has more digits, \(0.7\) is larger.
| \(\text{tenths}\) | \(:\) | \(3 = 3\) |
| \(\text{hundredths}\) | \(:\) | \(1 < 6\) |
| \(0.31\) | \(<\) | \(0.36\) |
The tenths are equal, so the hundredths decide. \(0.31\) is smaller.
| \(\text{each step}\) | \(=\) | \(1\text{ tenth}\) |
| \(4\text{ tenths}\) | \(=\) | \(0.4\) |
The arrow is 4 tenths from \(0\), so it points to \(0.4\).
| \(0.7\) | \(=\) | \(0.70\) |
| \(\text{tenths}\) | \(:\) | \(6 < 7\) |
| \(\text{then}\) | \(:\) | \(70 < 75\) |
Cheapest to dearest: $0.68, $0.70, $0.75.
Common pitfalls
Frequently asked questions
How do you compare two decimals?
Line up the decimal points and compare place by place, starting with the ones, then the tenths, then the hundredths. The first place where the digits differ decides which decimal is larger.
Which is bigger, 0.3 or 0.26?
\(0.3\) is bigger. Write \(0.3\) as \(0.30\), then compare: 3 tenths beats 2 tenths, so \(0.30 > 0.26\), even though \(0.26\) has more digits.
Does 0.4 equal 0.40?
Yes. A zero on the end does not change the value, because 4 tenths is the same as 40 hundredths. So \(0.4 = 0.40\).
How do you order decimals from smallest to largest?
Give every decimal the same number of places by adding a zero on the end where needed, then compare them two at a time from the left. Sort the list so the smallest is first.
Why is a decimal with more digits not always bigger?
Value comes from place, not from the number of digits. \(0.26\) has more digits than \(0.3\), but \(0.3 = 0.30\), which is larger. Compare places, not digit counts.
How do you compare decimals on a number line?
Mark each decimal on the line. The one further to the right is larger, and the one closer to \(0\) is smaller. To see which point is closest to a number, count the steps between them.