X Tables
Maths History

How the decimal point changed numbers

Connect decimal notation to money, measures and the challenge of writing tiny amounts.

Quick answer

The decimal point changed how we write numbers by showing where the whole numbers end and the parts begin, making it easy to write and understand numbers smaller than one, like 0.5 or 0.25.

Learning outcome

By the end of this page, you will understand how the decimal point helps us write numbers that are less than one, and how this system helps us measure, count, and share things more clearly. Success signs:
  • You can explain what the decimal point does in a number like 3.75
  • You can write numbers that are less than one using the decimal point
  • You can use the decimal point to measure things like length or weight
  • You can see how the decimal point makes sharing things fairer

Why this matters

Numbers that are less than one – like half a pizza or a quarter of a litre – are useful in real life. Without the decimal point, it would be hard to write these numbers clearly. The decimal point makes it easy to show where whole numbers stop and parts begin. It helps us do maths with money, cooking, science, and sports. It also helps us understand how to split things fairly, like sharing a cake or dividing a bag of sweets.

How it works

The decimal point is a small dot that sits between the whole number part and the part that is less than one. It shows where the units (ones) stop and where the tenths, hundredths, and so on begin. Let’s start with a simple example: Whole numbers: 1, 2, 3, 4, 5 Numbers with a decimal point: 1.5, 2.75, 3.2 The decimal point is always between the whole number and the part. For example, in 3.2: - The 3 is the whole number part (3 ones) - The 2 is the part (2 tenths) Each place after the decimal point is worth one-tenth of the place before it: - The first digit after the decimal point is the tenths place - The second digit is the hundredths place - The third digit is the thousandths place

Examples you can see

Let’s imagine you have a cake and want to share it fairly with your friend. Example 1: Sharing a cake If you cut the cake into 10 equal pieces and take 3 pieces, you have 3 tenths of the cake. That’s written as 0.3. Example 2: Measuring with a ruler A ruler shows centimetres and millimetres. If you measure something and it is 5 centimetres and 7 millimetres, it is written as 5.7 cm. Example 3: Money If you have 2 pounds and 50 pence, it is written as £2.50. The decimal point separates the pounds (whole numbers) from the pence (parts of a pound). Example 4: Cooking A recipe might say you need 0.5 litres of milk. This means half a litre. Without the decimal point, it would be hard to know that this is less than one litre.

Try it as a mini adventure

Adventure: The Decimal Point Detective You are a detective in a world where numbers are missing their decimal points. You must help the town’s shopkeeper, baker, and teacher by putting decimal points in the right places. Step 1: The shopkeeper has 120 pence, but writes it as 120. This is wrong! What should it be? Step 2: The baker says they need 350 grams of flour, but writes it as 350. What’s the correct way? Step 3: The teacher has 1000 points to share among 4 students. She writes it as 1000. What should she write instead? Step 4: You find a box with 500 pieces of candy. You want to share them equally among 10 friends. What is each friend’s share? Step 5: You have 3.5 metres of ribbon. You need to cut it into 5 equal pieces. How long is each piece? Step 6: You are measuring your height. You are 1.5 metres tall. How many centimetres is that? Step 7: You have 0.75 litres of juice. How many millilitres is that? Step 8: You are buying 2.25 kg of apples. How many grams is that? Step 9: You are reading a book that is 10.8 pages long. How many full pages and how many parts of a page? Step 10: You have 10.5 seconds to complete a race. How many tenths of a second is that?

Common mistakes

  • Mistake: Thinking 0.5 is bigger than 0.75. Why it happens: Children often think the bigger number in the decimal part makes the whole number bigger. Fix: Use a visual like a bar model or number line to show that 0.75 is 75 hundredths and 0.5 is 50 hundredths.
  • Mistake: Writing 2.5 as 25. Why it happens: The decimal point is forgotten or misunderstood. Fix: Explain that 2.5 means 2 whole and 5 tenths, not 25.
  • Mistake: Not understanding that 0.3 = 3/10. Why it happens: Confusion between decimal notation and fractions. Fix: Use fraction bars or pie charts to show that 0.3 is the same as 3/10.
  • Mistake: Writing 0.05 as 0.5. Why it happens: Misunderstanding place value. Fix: Use place value charts to show the difference between 0.5 and 0.05.

Parent and carer guide

Parents and carers can help by:
  • Using everyday examples like money, cooking, or shopping to talk about decimals.
  • Playing decimal games like "Decimal Snap" where you match decimals to fractions.
  • Using visual aids like number lines, pie charts, or bar models to show how decimals work.
  • Encouraging children to write decimals in different forms (e.g., 0.5 = 5/10 = 50/100).
  • Practising with real-life scenarios like measuring ingredients or splitting a pizza.
  • Not worrying if a child makes mistakes – these are learning moments!

Practice questions

  1. Write 4 tenths as a decimal.
  2. What is 0.75 written as a fraction?
  3. How many millilitres are in 0.25 litres?
  4. What is 3.5 metres in centimetres?
  5. Write 0.6 as a fraction.
  6. How many grams are in 0.75 kg?
  7. What is 0.8 as a fraction?
  8. How many centimetres are in 0.35 metres?
  9. What is 0.4 as a fraction?
  10. How many millilitres are in 0.5 litres?
Answers:
  1. 0.4
  2. 75/100 or 3/4
  3. 250 ml
  4. 350 cm
  5. 6/10 or 3/5
  6. 750 g
  7. 8/10 or 4/5
  8. 35 cm
  9. 4/10 or 2/5
  10. 500 ml

FAQ

What is the decimal point?

The decimal point is a small dot that separates the whole number part of a number from the part that is less than one.

Why do we need the decimal point?

The decimal point helps us write numbers that are less than one, like 0.5 or 0.25. Without it, we wouldn’t know where the whole number ends and the part begins.

How does the decimal point work?

Each digit after the decimal point has a place value. The first digit is the tenths place, the second is the hundredths place, and so on.

Where do we see decimals in real life?

We see decimals in money (like £2.50), measuring things (like 1.5 kg), cooking (like 0.5 litres), and sports (like 9.8 seconds).

Can decimals be more than one?

Yes! Decimals can be more than one. For example, 3.75 is 3 whole and 75 hundredths.