Topics · Primary Maths · Number & Place Value
Place value: what each digit is worth
A digit's value depends on where it sits. The 5 in 4,507 is worth five hundred; the 5 in 4,057 is worth fifty. Same digit, different column, different number.
- 408 exam papers analysed
- appears in 83% of P4 Maths papers
- ~3 min read
01 Position is the whole idea
We write every number with the same ten digits, 0 to 9. What makes 4,507 different from 4,057 is not the digits — they are the same four — but where each one sits.
Each column to the left is worth ten times the one on its right. Ones, tens, hundreds, thousands, and so on upward.
So the value of a digit is the digit multiplied by its column. The 5 below sits in the hundreds, so it is worth 5 × 100 = 500.
02 Zero holds the place
The 0 in 4,507 is not nothing. It is doing a job: holding the tens column empty so the 5 stays in the hundreds and the 7 stays in the ones.
Take it out and you get 457, a completely different number. That is why a nought in the middle of a number can never be dropped.
It is the same job the nought does in $4.05 and in 1.05 kg — holding a column so the digits either side keep their places.
03 Saying, writing and expanding
Papers ask for the same number in three forms, and want each written exactly.
- In figures: 4,507. Group in threes from the right so long numbers stay readable.
- In words: four thousand, five hundred and seven. No “and” before the thousands, and hyphens in numbers like thirty-four.
- In expanded form: 4000 + 500 + 7. The zero column contributes nothing, so it is simply left out of the sum.
- Value of a digit means digit × column — 500. The digit itself is just 5. Read which one the question wants.
04 Comparing, ordering and rounding
To compare two numbers, line them up by columns and read from the left. The first column where they differ decides it, whatever the digits after it do.
So 4,507 is bigger than 4,489, even though 89 is bigger than 07 — the hundreds column settled it before you reached them.
Rounding asks which of two numbers you are nearer to. Look at the digit after the place you are rounding to: 5 or more rounds up, less than 5 rounds down.
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- digitsayDIJ-itmore than onedigits
One of the ten symbols 0 to 9. A number is made of digits, and 4,507 has four.
- place value
What a digit is worth because of the column it sits in. The 5 in 4,507 has a place value of 500.
- expanded form
A number written as the sum of what each digit is worth: 4000 + 500 + 7.
- place holdermore than oneplace holders
A zero written to keep a column empty so the other digits stay where they belong, like the 0 in 4,507.
- roundmore than one—
To replace a number with a nearby simpler one. Look at the digit after the place you are rounding to: 5 or more rounds up.
- ascending ordersayuh-SEN-ding
Smallest first. Descending order is largest first.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P2
Numbers to 1,000: tens and ones, counting on, and comparing.
Practise P2 Number & Place Value — 10 questions →66% of P2 papers
- P3
Numbers to 10,000, place value of each digit, and ordering.
Practise P3 Number & Place Value — 10 questions →78% of P3 papers
- P4
Numbers to 100,000, rounding to the nearest 10, 100 and 1,000, and expanded form.
Practise P4 Number & Place Value — 10 questions →83% of P4 papers
- P5
Numbers to 10 million, and place value carried into decimals.
Practise P5 Number & Place Value — 10 questions →40% of P5 papers
- P6
Place value inside larger calculations and in estimation.
Practise P6 Number & Place Value — 10 questions →50% of P6 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“The value of the 5 in 4,507 is 5.”
That is the digit. Its value is 5 × 100 = 500. Papers ask for both and the words are different.
“4,057 — the nought does nothing, so it is 457.”
The nought holds the tens column empty. Remove it and every digit to its left slides down a place, giving a number ten times smaller.
“4,489 is bigger than 4,507 because 89 is bigger than 07.”
Compare from the left. The hundreds differ first — 5 against 4 — and that settles it before the last two digits matter.
“Four thousand and five hundred and seven.”
Only one “and”, before the last part: four thousand, five hundred and seven.
“4,507 to the nearest hundred is 4,600 because the 7 rounds up.”
Look at the digit after the hundreds column, which is the 0 in the tens. Zero is less than 5, so it rounds down to 4,500.
Now try it
50 questions across 5 levels, marked as you go with the working shown.