Expanded Form: Breaking Numbers Apart
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Expanded form writes a number as the sum of each digit’s place value: 139 = 100 + 30 + 9. Each part shows what one digit is really worth.
Why it works
Every digit is “how many” multiplied by “how much each one is worth”. In 139, the 3 is in the tens place, so it is 3 tens: 3 × 10 = 30. Do the same for every digit, then add the parts back together — you get the original number. Expanded form is simply place value written down. For the idea behind it, see what place value means.
Examples
- 246 = 200 + 40 + 6
- 731 = 700 + 30 + 1
- 1,394 = 1,000 + 300 + 90 + 4
- 12,507 = 10,000 + 2,000 + 500 + 7
Numbers with zeros
1,205 = 1,000 + 200 + 5. There is no tens part, because the tens place holds zero tens — and zero tens is worth 0, so we leave it out of the sum. The zero still matters in the written number: it keeps the 2 in the hundreds place. More zero examples are in understanding thousands.
Going backwards
From parts to a number: put each part in its place. 500 + 60 + 7 is 5 hundreds, 6 tens and 7 ones, so it is 567.
Try it: what is 3,000 + 40 + 2?
3 thousands, 0 hundreds, 4 tens, 2 ones: 3,042. Watch for the empty hundreds place.
Try it: write 8,306 in expanded form.
8,000 + 300 + 6 — there are zero tens, so there is no tens part.