Place value: what it is and how to help at home

What is place value?

Place value means that the position of a digit tells you what it's worth. The digit 4 is worth 4 in 34, 40 in 345 and 4,000 in 4,512. There are only ten digits, 0 to 9, but because each place is worth 10 times the one to its right, those ten digits can write any number.

The key fact children learn is that 10 of one place make 1 of the next: 10 ones make 1 ten, 10 tens make 1 hundred, and 10 hundreds make 1 thousand. Government guidance for teachers puts it as "100 is 10 times the size of 10", and children say sentences like that in class.

What place value charts show

A place value chart (sometimes called a place value grid) has a column for each place, with the biggest on the left. Writing a number in the chart shows what every digit is worth.

3,456 in a place value chart

Thousands	Hundreds	Tens	Ones
3	4	5	6

The same chart carries on past the ones into tenths and hundredths. The decimal point sits between the ones and the tenths, which is what lets us write decimals without drawing a chart at all.

34.56 in a place value chart

Tens	Ones	Tenths	Hundredths
3	4	5	6

In class, children often put place value counters on a chart: counters marked 1, 10, 100 or 1,000. Earlier on they use things they can bundle, such as ten straws tied together to make a ten. Both show that a ten really is ten ones, not just a digit in a different spot.

How place value grows through the school years

Every year group works with bigger numbers, and decimals come in from Year 4. This is what the national curriculum sets out:

Year	Numbers children work with
Year 1	Counting, reading and writing numbers to 100, and starting to see tens and ones in numbers beyond 20
Year 2	The value of each digit in a two-digit number (tens and ones), and zero as a place holder
Year 3	Three-digit numbers (hundreds, tens and ones), up to 1,000. Tenths come in through fractions
Year 4	Four-digit numbers (thousands, hundreds, tens and ones), and tenths and hundredths written as decimals
Year 5	Numbers to at least 1,000,000, and decimals with up to three places (thousandths)
Year 6	Numbers up to 10,000,000, and the value of each digit in numbers with up to three decimal places

The pattern never changes, so each year is the same idea stretched further. A child who really understands that 10 tens make a hundred has most of what they need for thousands, millions and tenths.

Zero as a placeholder

Zero holds a place open when there's nothing in it. In 305 there are no tens, but without the 0 the number would read 35. Children begin to understand zero as a place holder in Year 2.

305 in a place value chart

Hundreds	Tens	Ones
3	0	5

The chart makes the empty tens column easy to see. It's worth asking your child what the 0 is doing: "it shows there are no tens" is the answer to listen for.

Partitioning: splitting a number by place value

Partitioning means splitting a number into parts, usually by place value. 146 = 100 + 40 + 6 is the standard way. The curriculum also asks children to partition in other ways, such as 146 = 130 + 16, or 23 = 10 + 13, because that's what makes mental subtraction and column methods with exchanging work. There's more on this in our guide to partitioning numbers.

Multiplying and dividing by 10 and 100

When you multiply a number by 10, it becomes 10 times the size. The guidance for teachers uses exactly that language, and a sentence like this one:

"23, made 100 times the size, is 2,300. First we had 23 ones. Now we have 23 hundreds."

So 23 × 100 = 2,300. On a place value chart, each digit moves into the place 10 or 100 times bigger: one place to the left for × 10, two places for × 100. Dividing is the inverse: 1,450 ÷ 10 = 145, because "first we had 145 tens, now we have 145 ones", and each digit moves one place to the right.

This matters most with decimals. 3.4 × 10 = 34: the 3 ones become 3 tens and the 4 tenths become 4 ones. The decimal point stays between the ones and the tenths, and the digits move past it. Dividing works the same way: 34 ÷ 100 = 0.34.

Children divide one- and two-digit numbers by 10 and 100 in Year 4, then multiply and divide whole numbers and decimals by 10, 100 and 1,000 in Year 5 and Year 6.

Common place value mistakes

• "Just add a zero." It works for 23 × 10, but not for 3.4 × 10, which is 34, not 3.40. Thinking "10 times the size" works every time.
• Writing numbers as they sound. "Three hundred and five" written as 3005, because the child writes 300 and then 5. A place value chart sorts this out quickly.
• Comparing decimals by length. 0.35 isn't bigger than 0.4 just because 35 is bigger than 4. Compare the tenths first: 3 tenths is less than 4 tenths.
• Reading digits instead of values. Saying "the 6 in 4,612 is 6" instead of 600. Ask what it's worth, not what it is.
• Losing the zero. Missing out a placeholder, so 4,062 becomes 462.

How to teach place value at home

You don't need special equipment. A few minutes now and then with numbers your child sees anyway does a lot.

• Ask "what's that digit worth?" about house numbers, prices and page numbers.
• Use coins. £3.45 is 3 pounds, 4 ten pences and 5 pennies, which is ones, tenths and hundredths of a pound.
• Count in tens from any number. 17, 27, 37, 47: only the tens digit changes. Then try hundreds. A 10 times table practice round helps with this too.
• Make a place value chart for home. Draw columns on a sheet of paper, headed thousands, hundreds, tens and ones (add a point and tenths and hundredths for Year 4 and up). Write a number in it, then ask your child to make it 10 times the size and move the digits. Use bundles of straws or lolly sticks for younger children: ten singles swap for one bundle of ten.
• Use a number line as well. Place value tells you what a number is made of, and a number line shows where it sits among other numbers. Children need both.

Practice questions

1. What is the 7 worth in 3,742?
2. Write 4 thousands, 0 hundreds, 6 tens and 2 ones as a number.
3. What is 46 × 10?
4. What is 3,500 ÷ 100?
5. Which is bigger, 0.4 or 0.35?
6. What is 2.7 × 10?

Answers

1. 700
2. 4,062
3. 460
4. 35
5. 0.4
6. 27