Decimals: tenths, hundredths and decimal place value

What is a decimal?

A decimal is a way of writing a number that has a part smaller than one, using a decimal point. In 3.7 the 3 is whole ones and the 7 is 7 tenths, so 3.7 is a little less than 4. Decimals and fractions are two ways of writing the same amounts: 0.7 is ⁷⁄₁₀, and 0.25 is ²⁵⁄₁₀₀, which is a quarter.

The decimal point sits between the ones and the tenths. Government guidance for teachers explains that it's there so we can write these numbers without drawing a place value chart every time. One tenth is written 0.1 and one hundredth is written 0.01.

Children hear decimals said in two ways and need both. 0.36 is said "zero point three six" (or "nought point three six"), and it's also "3 tenths and 6 hundredths". Saying it the second way is what shows a child what the digits are worth.

Decimal place value: tenths, hundredths and thousandths

Decimal place value works exactly like whole numbers: each place is worth 10 times the place to its right. Past the ones, the places carry on getting smaller. A tenth is one whole split into 10 equal parts, a hundredth is a tenth split into 10, and a thousandth is a hundredth split into 10.

53.42 in a place value chart

Tens	Ones	Tenths	Hundredths
5	3	4	2

So 10 tenths make 1 one, and 10 hundredths make 1 tenth. Children learn to say "1 is 10 times the size of one tenth", the same kind of sentence they used for tens and hundreds. There's more on the chart itself in our guide to place value.

The order of the parts doesn't change the number. The guidance gives this example: 0.4 + 3 + 0.02 + 50 is 53.42, not 43.25, because each digit goes in the place it's worth. By Year 6 the chart has three decimal places:

2.375 in a place value chart

Ones	Tenths	Hundredths	Thousandths
2	3	7	5

What is one decimal place?

A decimal place is a place after the decimal point. A number with 1 decimal place, like 4.6, goes to tenths. A number with 2 decimal places, like 4.65, goes to hundredths, and 3 decimal places, like 4.652, goes to thousandths.

Money is the decimal most children see first. £3.45 has 2 decimal places: 3 pounds, 4 ten pences (tenths of a pound) and 5 pennies (hundredths of a pound). The curriculum brings in writing money as a decimal in Year 4.

Zeros on the end don't change the value. 0.5 is the same as 0.50, and 3 is the same as 3.0 or 3.00. That's useful when comparing decimals.

Ordering and comparing decimals

To compare decimals, line them up by the decimal point and compare the digits from the left, starting with the biggest place. In Year 4 children compare decimals with the same number of places, like 0.42 and 0.47. In Year 5 they order numbers with up to three decimal places, and that's where the mistakes creep in.

Worked example: put 0.4, 0.35, 0.405 and 0.3 in order, smallest first.

1. All four have 0 ones, so look at the tenths: 4, 3, 4 and 3.
2. 0.3 and 0.35 have 3 tenths, so they're the two smallest. 0.3 is 0.30, which has 0 hundredths, so it's smaller than 0.35.
3. 0.4 and 0.405 have 4 tenths. 0.4 is 0.400, so 0.405 is bigger by 5 thousandths.
4. In order: 0.3, 0.35, 0.4, 0.405.

Writing zeros on the end so every number has the same number of places (0.300, 0.350, 0.400, 0.405) makes this much easier to see. A number line helps too: 0.35 sits halfway between 0.3 and 0.4.

How do you make a percent a decimal?

To change a percentage to a decimal, divide it by 100. Per cent means "out of 100", so 45% is ⁴⁵⁄₁₀₀, and 45 hundredths is 0.45. In the same way, 7% is 7 hundredths, which is 0.07, and 50% is 0.5. Children learn this in Year 5.

The fractions, decimals and percentages guide has the ones worth knowing by heart, and how to work out percentages shows how to find a percentage of an amount.

How to turn a remainder into a decimal

A remainder can be written as a decimal by carrying on dividing past the decimal point. The national curriculum's own example is 98 ÷ 4. It's 24 with 2 left over, so 98 ÷ 4 = 24 remainder 2, which is also 24 and a half:

1. How many 4s in 9? 2, because 2 × 4 = 8, with 1 left over. Write 2 above and carry the 1 to the next digit.
2. The 1 ten carried makes 18 ones. How many 4s in 18? 4, because 4 × 4 = 16, with 2 left over. Write 4 above.
3. There are 2 left over at the end, so the answer is 24 remainder 2.

To carry on, write 98 as 98.0. The 2 ones left over are exchanged for 20 tenths, and 20 ÷ 4 = 5, so the answer has 5 tenths: 98 ÷ 4 = 24.5. In Year 6, children use written division where the answer has up to two decimal places. Short division (the bus stop method) and dividing decimals go through this step by step.

Recurring decimals

A recurring decimal is one whose digits go on for ever in a repeating pattern. A third is the best known: 1 ÷ 3 gives 0.3333..., with the 3s never stopping. In Year 6, children meet these when they change fractions into decimals by dividing, and they round them, often to three decimal places, so a third is about 0.333. Our page on fractions to decimals covers the fractions this happens with.

At secondary school: working out the exact fraction for a recurring decimal, such as 0.4444... as four ninths, is taught at key stage 4, not at primary.

Decimals through the school years

Year	What children learn about decimals
Year 3	Count up and down in tenths, as fractions, and link tenths to measures and dividing by 10
Year 4	Tenths and hundredths written as decimals, a quarter as 0.25 and three quarters as 0.75, dividing by 10 and 100, comparing decimals with the same number of places, money
Year 5	Thousandths, ordering decimals with up to three places, percentages as decimals, rounding decimals to the nearest whole number and to one decimal place, adding and subtracting decimals
Year 6	Every digit in numbers with up to three decimal places, multiplying decimals by whole numbers, dividing to give decimal answers, recurring decimals

Common mistakes with decimals

• Thinking longer means bigger. 0.35 isn't bigger than 0.4 because 35 is bigger than 4. Compare the tenths first, or write 0.4 as 0.40.
• Reading the digits as a whole number. Calling 0.25 "point twenty-five" can make it feel like 25. Saying "2 tenths and 5 hundredths" keeps the value clear.
• Dropping the zero placeholder. 4.07 and 4.7 are different numbers: 7 hundredths against 7 tenths.
• Adding a zero to multiply by 10. 3.4 × 10 = 34, not 3.40. The digits move one place to the left; the decimal point doesn't move.
• Lining up the last digits. When adding 4.5 and 2.25 in columns, line up the decimal points, not the right-hand ends.

How to help at home

• Use money. Prices are 2 decimal places. Ask how many pence £2.06 is, or which is more, £1.50 or £1.05.
• Use a tape measure or ruler. 1.4 metres is 1 metre and 4 tenths of a metre. Kitchen scales showing 0.75 kg do the same job.
• Say decimals both ways. "Zero point six", then "6 tenths".
• Order prices or times. Race times like 12.4 seconds and 12.38 seconds are good for ordering.

Practice questions

1. What is the 7 worth in 4.07?
2. Write 3 tenths and 4 hundredths as a decimal.
3. Put these in order, smallest first: 0.6, 0.06, 0.66, 0.606.
4. Write 35% as a decimal.
5. How many decimal places does 12.305 have?
6. Work out 17 ÷ 4 as a decimal.

Answers

1. 7 hundredths
2. 0.34
3. 0.06, 0.6, 0.606, 0.66
4. 0.35
5. 3
6. 4.25 (17 ÷ 4 = 4 remainder 1, and the 1 left over is a quarter)