The idea, step by step
Standard expanded form
Partitioning means splitting a number into parts that add back to the whole. In standard expanded form, each non-zero digit gets its own place-value part. For example, 58,126 = 50,000 + 8,000 + 100 + 20 + 6.
Add the parts to check. An empty place may appear as zero in a chart, but it does not need a separate + 0 term. Each non-zero part must still have the right place value.
Flexible partitions
A number has many correct partitions. The number 4,206 can be 4,000 + 206 or 4,100 + 100 + 6. Both sums describe the same whole.
Regroup one hundred as ten tens, or one thousand as ten hundreds. This is useful in calculations. The pieces change, but their total must stay exactly the same.
A common trap
Partitioning means writing the digits with plus signs between them.
Instead: Use digit values. The number 3,407 is 3,000 + 400 + 7, not 3 + 4 + 0 + 7.
See the thinking
Expand by place
Write 58,126 in standard expanded form.
- Read the value of each digit from the left.
- Combine 50,000, 8,000, 100, 20 and 6.
Regroup a hundred
Show 4,206 using 41 hundreds, some tens and 6 ones.
- 41 hundreds is 4,100. Calculate 4,206 − 4,100 − 6 = 100.
- 100 is 10 tens. Check: 4,100 + 100 + 6 = 4,206.
Check your understanding
Complete: 6,300 = 6 thousands + ___ hundreds.
Show answer
3
6,300 − 6,000 = 300, which is 3 hundreds.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- Write 46,825 in standard expanded form.1 mark
- What number is 6 thousands + 12 hundreds + 3 tens + 4 ones?1 mark
- Write 5,307 using hundreds, tens and ones.1 mark
- Complete: 7,615 = 75 hundreds + ___ tens + 5 ones.1 mark
- Sam writes 4,008 = 400 + 8. Explain and correct the error.2 marks
- Give two different partitions of 9,020.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Write 46,825 in standard expanded form.1 mark
Each part is the value of one non-zero digit.
40,000 + 6,000 + 800 + 20 + 5 - What number is 6 thousands + 12 hundreds + 3 tens + 4 ones?1 mark
6,000 + 1,200 + 30 + 4 = 7,234.
7,234 - Write 5,307 using hundreds, tens and ones.1 mark
5,300 is 53 hundreds; the remaining part is 7.
53 hundreds + 0 tens + 7 ones - Complete: 7,615 = 75 hundreds + ___ tens + 5 ones.1 mark
7,615 − 7,500 − 5 = 110, which is 11 tens.
11 - Sam writes 4,008 = 400 + 8. Explain and correct the error.2 marks
400 + 8 is 408, not 4,008.
The 4 means 4,000, so 4,008 = 4,000 + 8. - Give two different partitions of 9,020.2 marks
Both sums equal 9,020. Other equivalent partitions are valid.
For example, 9,000 + 20 and 8,000 + 1,020.
Curriculum reference & lesson scope
Australian Curriculum v9; SA Curriculum Mathematics 2026
Whole-number revision; partitioning; rounding/estimating quantities; checking reasonable answers.
Official curriculum source ↗