Decimals on a number line: what children learn
Year 4 introduces decimals. Pupils learn to recognise and write decimal equivalents of any number of tenths or hundredths, count in hundredths, and see that hundredths come from dividing one whole by 100 or a tenth by 10. 0.37 means 3 tenths and 7 hundredths, which is 37 hundredths.
The game uses two kinds of number line. One runs from 0 to 3 in tenths, with only the whole numbers labelled, for placing numbers such as 1.7. The other runs from 0 to 1 in hundredths, with bigger ticks for each tenth, for placing numbers such as 0.37. Because hundredths are so close together, being one hundredth out still counts on this line.
This topic covers the Year 4 statutory requirement in the National Curriculum in England (Number – fractions (including decimals)): pupils should be taught to “recognise and write decimal equivalents of any number of tenths or hundreds”. Year 4 pupils are usually aged 8–9. As published by the DfE; from the context this means tenths or hundredths.
For families following US standards, the closest Common Core standard is 4.NF.C.6, which is taught in Grade 4.
How to play
Move the marker to the right place on the number line, then press Check. You can drag, tap the line or use the arrow keys. Each game has 8 rounds. After you press Check, a green arrow shows the correct position if you were not quite right.
Step by step
- Work out what each step is worth. If one whole is split into 10 equal steps, each step is 0.1 (one tenth). If it is split into 100 steps, each is 0.01 (one hundredth).
- Find the whole number first. For 1.7, find 1, then count 7 tenths to the right.
- Use the tenths as signposts. For 0.37, find 0.3 (the third big tick), then count 7 small steps on towards 0.4.
- Check the size. 0.37 is less than a half (0.5), so it must be left of the middle.
Worked examples
Example 1: Put 2.4 on a 0 to 3 line in tenths.
Working: Find 2, then count 4 tenths to the right.
Answer: Four small steps after 2
Example 2: Put 0.82 on a 0 to 1 line in hundredths.
Working: Find 0.8 (the eighth big tick), then 2 small steps right.
Answer: Just past 0.8
Example 3: Put 0.05 on a 0 to 1 line in hundredths.
Working: Five hundredths is half of one tenth, so it is halfway between 0 and 0.1.
Answer: Between 0 and the first big tick
Common mistakes and how to fix them
- Thinking 0.5 is less than 0.37 because 5 is less than 37. Compare tenths first: 0.5 has 5 tenths, 0.37 has only 3.
- Treating every small tick as a tenth on a hundredths line. Count the small steps between 0 and 0.1. There are 10, so each is a hundredth.
- Reading 0.37 as 'nought point thirty-seven'. Say each digit after the point: 'nought point three seven'. This keeps the place values clear.
Activities to try at home
- Use money: £0.37 is 37p, and £1.70 is one pound seventy.
- Use a metre stick or tape measure: 0.45 m is 45 cm.
- Look at race times or temperatures with decimals and put them in order.
Ideas for the classroom
- Use a 'zoom in' number line: show 0 to 1 in tenths, then zoom in between 0.3 and 0.4 to show hundredths.
- Use hundred squares: shade 37 squares to show 0.37.
- Link to dividing by 10 and 100, which is also in the Year 4 programme of study.
Printable worksheet
The printable worksheet uses the same question generator as the game, so it practises exactly the same skills. It comes with a separate answer sheet on the second page. Print it, or save it as a PDF from your browser's print menu.
Frequently asked questions
What is the difference between tenths and hundredths?
A tenth is one whole split into 10 equal parts (0.1). A hundredth is one whole split into 100 equal parts (0.01). Ten hundredths make one tenth.
Why does being one hundredth out count as correct?
On a small screen, hundredths are only a few pixels apart, so the game accepts answers within one hundredth on that line. It shows the exact position afterwards.
Is the curriculum wording about 'hundreds' a mistake?
The published DfE text says 'decimal equivalents of any number of tenths or hundreds'. From the context and the rest of the programme of study, this clearly means hundredths.
What is the US equivalent?
Common Core 4.NF.C.6 (Grade 4): use decimal notation for fractions with denominators 10 or 100, and locate decimals such as 0.62 on a number line.