Numbers & the Number System • Topic 4 of 9

Expanded Form

Expanded form writes a number as the sum of the place values of its digits, making visible what each digit actually contributes. It is place value written out long-hand: 56 = 50 + 6, or stated fully 5 tens + 6 ones. The exam likes numbers with a zero, because that is where children stumble: 409 = 400 + 0 + 9, usually tidied to 400 + 9, where the zero tens simply add nothing. A four-digit case shows the full structure - 1234 = 1000 + 200 + 30 + 4, that is 1 thousand + 2 hundreds + 3 tens + 4 ones. The classic error is to expand by face value instead of place value, writing 321 = 3 + 2 + 1; the correction is 321 = 300 + 20 + 1, because the 3 is worth three hundreds and the 2 is worth two tens. Going the other way - collapsing 700 + 50 + 2 back to 752 - is the standard reverse task, and getting both directions fluent is what the exam checks.

✅ Solved examples

1. Write 56 in expanded form.
56 = 50 + 6, that is 5 tens + 6 ones.
2. Write 409 in expanded form.
409 = 400 + 0 + 9 = 400 + 9. The zero in the tens place contributes nothing, but it still holds the column.
3. Write 1234 in expanded form.
1234 = 1000 + 200 + 30 + 4, that is 1 thousand + 2 hundreds + 3 tens + 4 ones.
4. A child writes 321 = 3 + 2 + 1. Correct it and name the error.
The child expanded by face value, ignoring place value. Correct form: 321 = 300 + 20 + 1.

✏️ Practice — try these, take hints as needed

1. Write 78 in expanded form.
Seven tens, eight ones.
Two terms.
70 + 8
2. Write 605 in expanded form.
Six hundreds, zero tens, five ones.
The tens term is 0.
600 + 0 + 5 (or 600 + 5)
3. Combine 800 + 40 + 7 into a single numeral.
Read the place values off.
Three digits.
847
4. Write 2050 in expanded form.
Two thousands, zero hundreds, five tens, zero ones.
Two non-zero terms.
2000 + 50

📝 Topic test — 8 questions

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