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Place Value: What Each Digit Is Worth

In one line: Place value means a digit (one of the symbols 0 to 9) is worth a different amount depending on where it sits in a number, so the 3 in 30 is worth 3 tens, but the 3 in 300 is worth 3 hundreds.

Why it works

With only ten digits we can write any number at all, because each position, or place, is worth ten times the place to its right. Place value is how we read and write big numbers, compare them, and add, subtract, multiply and divide in columns. If place value is shaky, almost every later topic in number feels harder.

Think of it like: Imagine a sweet shop that sells single sweets, bags of 10 sweets and boxes of 100 sweets. If you have 2 boxes, 4 bags and 7 single sweets, you have 200 + 40 + 7 = 247 sweets. A written number works the same way: the hundreds place counts boxes, the tens place counts bags and the ones place counts single sweets. Whenever you collect 10 single sweets, you swap them for 1 bag, and 10 bags can be swapped for 1 box. (Where this breaks: In the shop you could keep 13 loose sweets, but in a written number each place can only hold one digit from 0 to 9, so as soon as you reach ten you must swap up to the next place. Also, an empty shelf in the shop is just empty, but in a written number an empty place must be filled with a 0, called a placeholder, or the other digits slide into the wrong places.)

Worked example

In the number 3,405, what is each digit worth? Write the number in expanded form (as a sum of the values of its digits).

  1. Write the place names from right to left: ones, tens, hundreds, thousands.
  2. Put each digit under its place: 3 is in the thousands, 4 is in the hundreds, 0 is in the tens, 5 is in the ones.
  3. Work out each value: 3 thousands = 3,000; 4 hundreds = 400; 0 tens = 0; 5 ones = 5.
  4. Notice the 0 is a placeholder: it shows there are no tens and keeps the 3 and 4 in their correct places.
  5. Add the values to write expanded form: 3,000 + 400 + 0 + 5 = 3,405.

Answer: The 3 is worth 3,000, the 4 is worth 400, the 0 is worth 0 and the 5 is worth 5, so 3,405 = 3,000 + 400 + 5.

Common mistakes

  • Saying a digit is worth only its face value, such as calling the 5 in 352 'five'; fix this by naming the place first, so it becomes '5 tens, which is 50'.
  • Leaving out a zero placeholder, such as writing four hundred and six as 46; fix this by drawing a hundreds, tens and ones chart and putting a 0 in any empty column.
  • Writing numbers exactly as they sound, such as writing three hundred and twenty-five as 30025; fix this by remembering that a three-digit number has only three digits and filling the chart place by place.
  • Thinking the number with the biggest first digit is always larger, such as believing 89 is bigger than 102; fix this by counting the digits first, because a number with more digits (and no leading zeros) is bigger.

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What is the value of the 6 in 362?

Questions parents ask

What year do kids learn place value?

Children start with tens and ones around Year 1 to Year 2 in the UK and Australia, and Grade 1 in the US. Hundreds usually follow in Year 2 to Year 3 (Grade 2 in the US), and thousands in Year 3 to Year 4. Place value then keeps growing to millions and decimals in later years.

How can I help my child with place value at home?

Use real objects: bundle straws or lolly sticks into tens with elastic bands, or use 1p, 10p and £1 coins to build numbers. Ask questions like 'What is the 4 worth in 245?' and practise swapping 10 ones for 1 ten. Short, regular chats about numbers on prices, house numbers and car plates help a lot.

Why is zero so important in place value?

Zero acts as a placeholder, showing that a place is empty while keeping the other digits in the right positions. Without it, 307 would become 37, which is a very different number. Children often find this tricky, so it is worth practising numbers like 405, 1,060 and 2,008.

What is expanded form?

Expanded form means writing a number as the sum of the values of its digits, for example 647 = 600 + 40 + 7. It shows clearly what each digit is worth. Schools may also call this partitioning a number.