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decimals

Ordering decimals

Arrange decimals using tenths, hundredths and zero placeholders.

Quick answer

Ordering decimals means putting decimal numbers in order from smallest to largest (ascending) or largest to smallest (descending). You compare the digits in each place value, starting with the tenths place, then hundredths, and so on.

Learning outcome

By the end of this page, you will be able to compare and order decimal numbers with tenths and hundredths. Success signs:
  • You can tell which decimal is bigger or smaller
  • You can arrange decimals from smallest to largest
  • You understand how zeros in decimal places work
  • You can use a place value chart to help you

Why this matters

Decimals are used everywhere in everyday life! When you go shopping and see prices like £2.99 or £1.50, you're using decimals. When you measure ingredients for a recipe, like 0.5 litres of milk or 0.25 kg of sugar, you're working with decimals. When you time yourself running, you might get 12.34 seconds. Learning to order decimals helps you understand money, cooking, sports times, and many other things you do every day.

How it works

To order decimals, follow these steps:
  1. Look at the whole number part first (if there is one)
  2. Compare the tenths place (the first digit after the decimal point)
  3. If the tenths are the same, look at the hundredths place (the second digit after the decimal point)
  4. If the hundredths are the same, look at the thousandths place (the third digit after the decimal point)
  5. Continue comparing places until you can tell which is bigger

Examples you can see

Let's look at some decimal numbers and see how to order them:
  • 0.4, 0.35, 0.52, 0.2
Let's line them up in a place value chart:
Whole number Tenths Hundredths
0 4 0
0 3 5
0 5 2
0 2 0
Now we can compare:
  • 0.2 has 2 tenths, so it's the smallest
  • 0.35 has 3 tenths, so it's next
  • 0.4 has 4 tenths, so it's next
  • 0.52 has 5 tenths, so it's the largest
So in order from smallest to largest: 0.2, 0.35, 0.4, 0.52 Here's another example with more numbers:
  • 1.23, 1.3, 1.2, 1.35
We line them up:
Whole number Tenths Hundredths
1 2 3
1 3 0
1 2 0
1 3 5
We start with the whole number part - all are 1, so we move to tenths:
  • 1.2 and 1.23 both have 2 tenths
  • 1.3 and 1.35 both have 3 tenths
Now we compare the hundredths:
  • 1.2 has 0 hundredths, so it's smaller than 1.23
  • 1.3 has 0 hundredths, so it's smaller than 1.35
So in order from smallest to largest: 1.2, 1.23, 1.3, 1.35

Try it as a mini adventure

Adventure: The Decimal Race You are a race car driver who needs to collect decimal cards to win a race. Each card has a decimal number on it. You need to arrange them from smallest to largest to get the fastest route to the finish line. You have these decimal cards:
  • 0.8
  • 0.85
  • 0.75
  • 0.9
  • 0.7
Your challenge: Arrange these from smallest to largest to help your car win the race. First, look at the tenths place:
  • 0.7 and 0.75 have 7 tenths
  • 0.8 and 0.85 have 8 tenths
  • 0.9 has 9 tenths
Next, compare the hundredths:
  • 0.7 has 0 hundredths
  • 0.75 has 5 hundredths
  • 0.8 has 0 hundredths
  • 0.85 has 5 hundredths
  • 0.9 has 0 hundredths
So the order from smallest to largest is:
  1. 0.7
  2. 0.75
  3. 0.8
  4. 0.85
  5. 0.9
You've won the race! Your car will take the fastest path with these decimal numbers in order.

Common mistakes

  • Mistake: Thinking 0.5 is bigger than 0.45 because 5 is bigger than 4.
    Why it happens: Children often look at the first digit after the decimal point and forget to look at the hundredths place.
    Fix: Always look at each place value from left to right. 0.45 has 4 tenths and 5 hundredths, so it's smaller than 0.5 which has 5 tenths and 0 hundredths.
  • Mistake: Ignoring zeros in decimal numbers.
    Why it happens: Some children think 0.2 is the same as 0.20 because they see the same digits.
    Fix: Remember that 0.2 = 0.20. Both have 2 tenths and 0 hundredths, so they are equal.
  • Mistake: Comparing decimals like 1.23 and 1.3 by looking at the last digit.
    Why it happens: Children get confused when the whole number parts are the same and they focus on the last digit.
    Fix: Always compare from left to right. 1.3 is the same as 1.30, so 1.30 is bigger than 1.23.

Parent and carer guide

You can help your child practice ordering decimals in many fun ways:
  • Use everyday items like money or measuring cups to show decimals in real life
  • Play the decimal ordering game together with cards or number lines
  • Ask your child to order prices from a shop or menu
  • Use a place value chart to help them see the decimal parts clearly
  • Encourage them to explain their thinking out loud
Remember:
  • It's okay if they make mistakes - they're learning!
  • Keep the practice short and fun
  • Focus on understanding, not just getting the right answer
  • Use real-world examples they can relate to

Practice questions

  1. Order these decimals from smallest to largest: 0.4, 0.35, 0.52, 0.2
  2. Order these decimals from largest to smallest: 1.3, 1.23, 1.35, 1.2
  3. Which decimal is the smallest: 0.6, 0.58, 0.62, 0.5
  4. Order these decimals from smallest to largest: 2.1, 2.05, 2.15, 2.0
  5. Which decimal is the largest: 0.75, 0.8, 0.7, 0.85
Answers:
  1. 0.2, 0.35, 0.4, 0.52
  2. 1.35, 1.3, 1.23, 1.2
  3. 0.5
  4. 2.0, 2.05, 2.1, 2.15
  5. 0.85

FAQ

What does it mean to order decimals?

Ordering decimals means arranging decimal numbers in a sequence - either from smallest to largest (ascending) or largest to smallest (descending).

How do I know which decimal is bigger?

You compare the digits in each place value, starting from the left. First compare whole numbers, then tenths, then hundredths, and so on.

Why is 0.5 bigger than 0.45?

0.5 is the same as 0.50. It has 5 tenths and 0 hundredths, while 0.45 has 4 tenths and 5 hundredths. So 0.5 is bigger.

Can I add zeros to decimals?

Yes! 0.5 is the same as 0.50. Adding zeros at the end doesn't change the value of the decimal.

How can I practice ordering decimals at home?

You can use money, cooking measurements, or even play a game with decimal cards. Try ordering prices from a menu or measuring ingredients for a recipe.