Year 4 maths · Key Stage 2 · Number – fractions (including decimals)

Year 4 decimals: tenths, hundredths and rounding

In Year 4 children discover that decimals are simply another way of writing fractions. They learn that 0.3 means 3/10 and 0.07 means 7/100, that 0.5, 0.25 and 0.75 are the decimal names for 1/2, 1/4 and 3/4, and that dividing by 10 or 100 makes each digit worth a tenth or a hundredth as much. They also round, compare and use decimals in money and measures.

Decimals: tenths and hundredths, explained

A decimal point separates the whole numbers from the parts of a whole. Everything to the left of the point is worth ones, tens, hundreds and so on, as usual. Everything to the right is smaller than one. The first place after the point is tenths, because one whole has been cut into 10 equal parts, and the second place is hundredths, because each tenth has been cut into 10 again. So 0.3 is 3/10, 0.07 is 7/100 and 0.47 is 47/100, which is 4 tenths and 7 hundredths. Children in Year 4 read and write the decimal equivalent of any number of tenths or hundredths, usually with a place value chart that has columns for ones, tenths and hundredths.

Three fractions get special attention: 1/2, 1/4 and 3/4. Children learn that 1/2 is 5/10, or 50/100, so it is written 0.5. A quarter is 25/100, so 1/4 is 0.25, and three quarters is 75/100, so 3/4 is 0.75. Money makes these easy to believe. A quarter of a pound is 25p, three quarters is 75p, and the pence are just hundredths of a pound. A metre stick works the same way, with 25 centimetres being a quarter of a metre, or 0.25 m.

Dividing by 10 and 100 is where place value and decimals meet. When a one- or two-digit number is divided by 10, every digit is worth a tenth of what it was, so it moves one place to the right: 6 ones become 6 tenths, so 6 ÷ 10 = 0.6. Dividing by 100 moves each digit two places to the right, so 47 ÷ 100 = 0.47, with the 4 tens now worth 4 tenths and the 7 ones now worth 7 hundredths. Many teachers describe the digits moving, not the decimal point, because the point stays fixed as the marker between the ones and the tenths.

The same ideas support three more skills. Children round a number with one decimal place to the nearest whole number, by asking whether it is closer to the whole number below or above: 4.3 rounds to 4, and 4.6 rounds to 5. A number exactly halfway, such as 4.5, rounds up to 5. They compare and order numbers with the same number of decimal places, up to two, looking at the ones first, then the tenths, then the hundredths. And they solve simple money and measure problems, such as finding the change from a £5 note or adding 1.25 m to 0.75 m. Counting forwards and backwards in steps of 0.1 or 0.25 on a number line helps all of this to stick.

Words your child will hear

Decimal point: The dot that separates whole numbers from parts of a whole, as in 3.4.
Tenth: One of 10 equal parts of a whole. It is written 1/10 or 0.1.
Hundredth: One of 100 equal parts of a whole. It is written 1/100 or 0.01.
Decimal place: A digit’s position after the point. 0.47 has two decimal places.
Decimal equivalent: The same amount written as a decimal, such as 0.75 for 3/4.
Round: Replace a number with a nearby, simpler one, such as 4.6 to 5.
Place value chart: A table with a column for each place, used to show where each digit sits.

What the National Curriculum says

In Year 4, pupils should be taught to:

Recognise and write decimal equivalents of any number of tenths or hundredths
Recognise and write decimal equivalents to 1/4, 1/2, 3/4
Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
Round decimals with 1 decimal place to the nearest whole number
Compare numbers with the same number of decimal places up to 2 decimal places
Solve simple measure and money problems involving fractions and decimals to 2 decimal places

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Work out 35 ÷ 100 and say what each digit in the answer is worth.

Start with place value. 35 is 3 tens and 5 ones. Estimate first: 35 is less than 100, so dividing it by 100 must give an answer smaller than 1.
```
    T  O  .  t   h
    3  5
```
Dividing by 100 makes every digit worth a hundredth of what it was, so each digit moves two places to the right. The 3 tens move to the tenths column: 30 ÷ 100 is 3 tenths.
The 5 ones move two places to the hundredths column: 5 ÷ 100 is 5 hundredths.
The ones place is now empty, so write a 0 there and put the decimal point after it.
```
    T  O  .  t   h
       0  .  3   5
```
Check: 0.35 is 35/100, which matches 35p out of £1, so the answer makes sense.

35 ÷ 100 = 0.35. The 3 is worth 3 tenths and the 5 is worth 5 hundredths.

Common mistakes and how to help

Mixing up tenths and hundredths, so 0.05 is read as 5 tenths

Children often see the 5 and ignore the zero in front of it. The same thing happens with money, where 5p gets written as £0.5 instead of £0.05.

What helps: Always use a place value chart. The zero in 0.05 holds the tenths place, so the 5 sits in the hundredths. Link it to pence: £0.05 is 5p, not 50p.

“Dividing by 10 takes a zero off”

This works for 40 ÷ 10 = 4, so children apply it to 4 ÷ 10 and look for a zero that isn’t there. Others add a point and a zero and write 4.0.

What helps: Describe it as each digit moving one place to the right. 4 ones become 4 tenths, so 4 ÷ 10 = 0.4. Use coins: 4 pounds shared among 10 people gives 40p each.

Rounding 4.6 down to 4, or 4.5 down to 4

Some children only look at the whole number and ignore the tenths. Others are unsure what to do when a number is halfway.

What helps: Place the number on a number line between 4 and 5 and ask which end it is nearer to. Explain the rule for the halfway number: 4.5 rounds up to 5.

Choosing the larger number because its digits after the point are bigger

Faced with 2.9 and 3.1, a child sees 9 and 1 and decides 2.9 must be bigger, forgetting to look at the ones first.

What helps: Compare from the left: ones, then tenths, then hundredths. Here 3 ones beats 2 ones, so 3.1 is bigger. A number line, or lengths in metres, makes it clear.

How to help at home

Talk in pounds and pence. Prices are decimals with two places. Ask what fraction of a pound 30p is (30/100, which is the same as 3/10, or 0.3), or what you would pay for four items at £1.25 each.
Use a ruler or metre stick. Read lengths as decimals of a metre: 40 cm is 0.4 m and 7 cm is 0.07 m. Measuring a table or a doorway gives plenty of tenths and hundredths to practise on.
Chalk a number line. Draw a line from 0 to 1 on paper, or in chalk on a patio or playground, marked in tenths. Count along in 0.1s, then in 0.25s, and place numbers such as 0.5, 0.75 and 0.3 where they belong.
Round at the shop. Look for prices that end in a zero, such as £1.80 or £3.40, which are 1.8 and 3.4 pounds, and ask your child to round each to the nearest pound. Lengths such as 1.6 m and weights such as 2.3 kg work just as well. Rounding a few items and adding gives a quick estimate of the total.
Divide by 10 and 100 with money. Use pretend sums: £3 shared between 10 people is 30p each, so 3 ÷ 10 = 0.3. £25 shared between 100 people is 25p each, so 25 ÷ 100 = 0.25. Ask your child to say each answer as a decimal and as a fraction.

Builds on

Year 3: Tenths and equivalent fractions

Leads on to

Year 5: Mixed numbers and fraction calculations
Year 5: Decimals, thousandths and percentages