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decimals

Comparing decimals

Use place value, not length of the number, to compare decimals.

Quick answer

When comparing decimals, look at the place value of each digit, not how long the decimal looks. The decimal with the larger digit in the first place where they differ is the bigger number.

Learning outcome

By the end of this page, you will be able to compare decimals using place value and decide which one is bigger or smaller. Success signs:
  • You can look at two decimals and tell which one is bigger.
  • You know that 0.5 is bigger than 0.3, even though 0.3 has more digits.
  • You can use place value to compare decimals like 0.75 and 0.7.
  • You can explain why one decimal is bigger than another.

Why this matters

Comparing decimals helps you in many real-life situations. When you go shopping and need to find the cheaper item, or when you are cooking and need to measure ingredients, you use decimals. In sports, times are often given as decimals, like 10.5 seconds. If you want to know who ran faster, you compare these times. In science, measurements are often decimals too, like 3.75 kg or 2.25 m. Knowing how to compare decimals helps you make good decisions every day.

How it works

To compare decimals, follow these steps:
  1. Look at the whole number part first. If they are different, the one with the bigger whole number is bigger.
  2. If the whole numbers are the same, line up the decimal points and compare digits from left to right.
  3. Start comparing at the tenths place (the first digit after the decimal point).
  4. If the tenths are the same, move to the hundredths place (the second digit after the decimal point).
  5. Keep going until you find a difference.

Examples you can see

Let's try some examples together. Example 1: Compare 0.4 and 0.6
  • Both numbers have 0 as the whole number part.
  • Compare the tenths place: 4 and 6.
  • Since 6 is bigger than 4, 0.6 is bigger than 0.4.
Example 2: Compare 0.37 and 0.32
  • Both numbers have 0 as the whole number part.
  • Compare the tenths place: both are 3.
  • Move to the hundredths place: 7 and 2.
  • Since 7 is bigger than 2, 0.37 is bigger than 0.32.
Example 3: Compare 1.2 and 1.09
  • Both numbers have 1 as the whole number part.
  • Compare the tenths place: 2 and 0.
  • Since 2 is bigger than 0, 1.2 is bigger than 1.09.
Example 4: Compare 0.8 and 0.80
  • Both numbers have 0 as the whole number part.
  • Compare the tenths place: both are 8.
  • Compare the hundredths place: 0 and 0.
  • These decimals are equal. 0.8 is the same as 0.80.

Try it as a mini adventure

Imagine you and your friend are at a sweet shop. You both want to buy some candy, but you have different amounts of money. You have £1.25 and your friend has £1.30. You need to figure out who can buy more candy.
  1. Look at the whole number parts: both are 1.
  2. Compare the tenths place: 2 and 3.
  3. Since 3 is bigger than 2, your friend has more money.
  4. Your friend can buy more candy!
You can also imagine this as a race. You are running a 1.25 km race and your friend is running a 1.30 km race. Who runs further? You can use the same method to compare these distances.

Common mistakes

  • Mistake: Thinking that 0.5 is smaller than 0.3 because 0.5 has more digits.
    Why it happens: Children sometimes think more digits mean more value.
    Fix: Remember to look at the place value of each digit. In 0.5, the 5 is in the tenths place, which is bigger than the 3 in 0.3.
  • Mistake: Comparing 0.4 and 0.40 and thinking they are different.
    Why it happens: Some children think that 0.40 looks bigger because it has more digits.
    Fix: 0.4 and 0.40 are the same. The 0 at the end of 0.40 doesn't change the value.
  • Mistake: Comparing 0.7 and 0.75 by looking at the hundredths place first.
    Why it happens: Children may not understand the order of place value.
    Fix: Always start comparing from the left, beginning with the tenths place.

Parent and carer guide

Parents and carers can help by:
  • Using real-life examples like money, cooking, or shopping to show how decimals are used.
  • Practicing with visual aids like base ten blocks or decimal squares.
  • Encouraging children to explain their thinking out loud when comparing decimals.
  • Reinforcing that place value is key, not the number of digits.
  • Using games or apps that involve comparing decimals to make learning fun.
At home, you can:
  1. Play a game where you compare prices of items in a shop or online.
  2. Use cooking to show how decimals work (e.g., 0.5 kg of flour vs 0.75 kg).
  3. Ask your child to compare times, distances, or weights using decimals.
  4. Use a number line to show where decimals sit in relation to each other.

Practice questions

  1. Which is bigger: 0.3 or 0.4?
  2. Compare 0.67 and 0.65. Which is bigger?
  3. Which is smaller: 0.9 or 0.90?
  4. Compare 1.2 and 1.19. Which is bigger?
  5. Which is bigger: 0.56 or 0.6?
Answers:
  1. 0.4
  2. 0.67
  3. They are equal (0.9 = 0.90)
  4. 1.2
  5. 0.6

FAQ

Why do we compare decimals using place value?

We compare decimals using place value because it helps us understand how much each digit actually represents. For example, in 0.5, the 5 is worth 5 tenths, while in 0.05, the 5 is worth only 5 hundredths.

What happens if decimals have different numbers of digits?

It doesn't matter how many digits there are. You still compare from left to right using place value. If one decimal doesn't have a digit in a certain place, you can think of it as 0.

Can I add zeros to decimals to make them easier to compare?

Yes! Adding zeros at the end of a decimal doesn't change its value. For example, 0.5 = 0.50 = 0.500. This can help when comparing.

How do I know which decimal is bigger when they look the same?

If decimals look the same but have different numbers of digits, compare the place value. For example, 0.4 = 0.40, so they are equal.

Is there a quick way to remember how to compare decimals?

Yes! Think of it like reading a story. Start from the beginning (the whole number part) and move to the right (the decimal places). The first difference you see tells you which is bigger.