The idea, step by step
A digit gets its value from its place
The same digit can stand for different amounts. In 4,825, the 4 means four thousands, not four ones. Moving one place to the left makes a place ten times as large. Read a large number in groups: thousands, then hundreds, tens and ones.
A zero holds a place when there are no units of that size. In 40,206, the zero after 4 keeps the 4 in the ten-thousands place. The other zero shows there are no tens. Do not drop these zeroes when writing the number.
| Ten-thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 4 | 0 | 2 | 0 | 6 |
Different ways to build the same number
Expanded form shows the value of each non-zero digit. For 4,825, write 4,000 + 800 + 20 + 5. Adding those parts rebuilds the original number.
Exchange ten units of one place for one of the next place. For example, 3 hundreds and 6 tens is also 36 tens. Regrouping changes how we describe a number, not its amount. This idea is useful in addition and subtraction.
A common trap
Saying the 6 in 6,028 is worth 6.
Instead: Name its place as well as the digit. It is in the thousands place, so its value is 6,000.
See the thinking
Find a digit value
What is the value of 7 in 27,413?
- Read the place headings from the right: ones, tens, hundreds, thousands, ten-thousands.
- The 7 is in the thousands place. It represents 7 groups of 1,000.
- 7 × 1,000 = 7,000.
Rename a number
Write 2,340 as hundreds, tens and ones, without using thousands.
- Exchange the 2 thousands for 20 hundreds.
- Add the 3 hundreds already in the number: 20 + 3 = 23 hundreds.
- Keep the 4 tens and 0 ones. Check: 2,300 + 40 = 2,340.
Check your understanding
In 50,407, what is the value of 4?
Show answer
400.
The 4 is in the hundreds place. The zero in the tens place does not move it.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- Write 6,302 in words.1 mark
- What is the value of 8 in 18,245?1 mark
- Write 7,064 in expanded form.1 mark
- Build a number from 3 ten-thousands, 2 thousands, 5 hundreds, 0 tens and 9 ones.1 mark
- Write 4,120 using hundreds, tens and ones but no thousands.2 marks
- A learner writes 20,306 as 2,000 + 300 + 6. Explain the error and correct it.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Write 6,302 in words.1 mark
Read the thousands first, then the hundreds and remaining ones.
Six thousand three hundred and two. - What is the value of 8 in 18,245?1 mark
The 8 is in the thousands place: 8 × 1,000 = 8,000.
8,000. - Write 7,064 in expanded form.1 mark
The digits mean 7 thousands, 0 hundreds, 6 tens and 4 ones.
7,000 + 60 + 4. - Build a number from 3 ten-thousands, 2 thousands, 5 hundreds, 0 tens and 9 ones.1 mark
30,000 + 2,000 + 500 + 9 = 32,509.
32,509. - Write 4,120 using hundreds, tens and ones but no thousands.2 marks
Exchange 4 thousands for 40 hundreds, then add the existing hundred.
4,100 + 20 = 4,120.
41 hundreds, 2 tens and 0 ones. - A learner writes 20,306 as 2,000 + 300 + 6. Explain the error and correct it.2 marks
The 2 is in the ten-thousands place, not the thousands place.
Keep the empty thousands and tens places when rebuilding the number.
The 2 is worth 20,000. Correct form: 20,000 + 300 + 6.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Place-value revision; odd/even properties; addition/subtraction strategies; missing values; rounding/checking.
Official curriculum source ↗