Decimals
A decimal is a number with a decimal point separating whole units from parts smaller than one, based on tenths, hundredths and so on.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
A decimal is a number with a decimal point separating whole units from parts smaller than one, based on tenths, hundredths and so on.
- Digits after the point are tenths, hundredths, thousandths
- Line up decimal points to add and subtract
- Multiplying by 10 moves digits one place left
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Decimals?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Decimals. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Decimals in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Decimals gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Decimals in detail
Decimals extend place value to the right of the decimal point, where the places are tenths, hundredths, thousandths and so on, each ten times smaller than the one before. So 3.47 means 3 units, 4 tenths and 7 hundredths.
To compare decimals, line up the decimal points and compare digit by digit from the left, so 0.7 is larger than 0.07 and 0.45 is larger than 0.405. Decimals are used for money, measurements and calculator results, and they can be added, subtracted, multiplied and divided with careful attention to the position of the decimal point.
How the interactive helps you understand Decimals
Watch the bar chart in the interactive. Use any sliders or buttons it offers to change the values and see how the bar chart responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Decimals.
Real-life uses and examples
- Explain Decimals to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Decimals in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Decimals by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Decimals without checking why they work.
- Forgetting units, signs or brackets when you apply Decimals.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Decimals
What is Decimals?
A decimal is a number with a decimal point separating whole units from parts smaller than one, based on tenths, hundredths and so on.
What are the most important points about Decimals?
The main points are: Digits after the point are tenths, hundredths, thousandths; Line up decimal points to add and subtract; Multiplying by 10 moves digits one place left.
Why is Decimals useful?
Understanding Decimals gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Decimals?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Decimals?
Related topics in Mathematics include Percentage Change, Proportion, Laws of Indices.