The idea in brief. Write every number to the same number of decimal places first, padding with noughts, and then compare digit by digit from the greatest place down, exactly as with whole numbers. More digits does not mean bigger: 7.06 is smaller than 7.6, because 7.60 beats 7.06 at the tenths.
Lesson video, with the working
Comparing and ordering decimals
2 min 50 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
the digits in the ones place of both numbers are the same
0.9 = 0.90
compare the digits in the tenths place
9 > 8
so 0.90 > 0.86, and the greater number = 0.9
Ans: 0.9
Example 1
In the decimal 5.___24, the digit in the tenths place is hidden. The decimal is smaller than 5.324. What is the greatest digit that can go in the hidden place?
the digits in the ones place of both numbers are the same
compare the digits in the tenths place
5.324 has 3 in the tenths place
the hidden digit must be smaller than 3, so the greatest possible digit = 2
Ans: 2
How to solve it
Compare matching places, starting at the greatest place. Both decimals have 0 ones.
Write 0.9 as 0.90. The value stays the same.
Compare tenths: 9 is greater than 8, so 0.90 is greater than 0.86.
Stop at the first unequal place. The hundredths do not change this comparison.
For a hidden tenths digit, compare it with the 3 tenths in 5.324. The other places match.
The hidden digit must be smaller than 3. The greatest possible digit is 2.
Start at the greatest place. The first unequal digit decides.
Practice questions with worked solutions
Question 1 is free to try. The other 6 open in the free trial, each with its full working.
2.475 and 2.480 have the same tenths digit; compare the hundredths
7 < 8, so 2.475 < 2.480
2.480 < 2.500
arranged in ascending order: 2.475, 2.48, 2.5
Answer: 2.475, 2.48, 2.5
For parents
How can I help my child with comparing decimals of different lengths?
Your child compares decimal values by the size of their parts, beginning with the whole-number part.
What your child learns here
Your child compares decimal values by the size of their parts, beginning with the whole-number part. This follows the MOE P4 outcome on comparing and ordering decimals up to three decimal places. It also helps your child explain why a decimal with more written digits is not necessarily the greater number.
Compare the whole-number parts first, then check tenths, hundredths and thousandths until reaching the first place where the values differ.
Recognise equivalent decimals with trailing zeros, and use these forms to compare matching places when two numbers have different lengths.
Arrange a collection in ascending order, from smallest to greatest, or descending order, from greatest to smallest, as the question requests.
Choose a decimal that satisfies both a lower and an upper limit, explaining each comparison rather than testing only one side.
Describe the change between neighbouring terms in a decimal sequence and check that the proposed next term follows the same stated pattern.
Does the answer make sense?
In the comparison 0.7 and 0.68, writing seven tenths as seventy hundredths shows that 0.7 is greater. If your child's ascending list places 0.7 before 0.68, comparing those two entries in hundredths reveals that their order needs to be reversed.
How to practise these questions
Basic practice covers ordering a short list and recognising two equivalent decimal forms. The Intermediate questions place masses in ascending or descending order and continue a decimal sequence that crosses a whole number. Challenge questions ask your child to identify a correctly ordered list or form possible decimals from given digits that can occupy a particular place in a descending list. Work through a close pair by naming the first place that differs, then check the requested direction of the full list. For a digit-arrangement question, ask your child to test both the digit-use conditions and the comparison, so a valid arrangement also fits its required position.
Questions parents ask
Why can a shorter decimal be greater than a longer one? The places carry different values, so counting digits after the point does not measure the number's size. Seven tenths is greater than six tenths and eight hundredths. Once the tenths decide this comparison, the extra hundredths do not reverse it.
Can my child add zeros when comparing decimal numbers? Yes, at the right-hand end of the decimal part. This gives an equivalent form with the same number of decimal places as the other value. Inserting a zero between existing digits can change their places and therefore the amount, so ask your child to explain where the zero goes.
How can I check whether my child understands an ordered list? Ask which place decides the order of two neighbouring numbers, especially when their whole-number parts match. Then ask your child to read the direction requested in the question. Explaining one close pair gives more information about their place-value understanding than simply reading the finished list aloud.
