Understand the idea.
A digit gets its value from its place
Read a number from right to left to find each place: ones, tens, hundreds, thousands, then ten-thousands. In , the digit counts thousands, so its value is . Each place holds units ten times the size of the place beside it on the right.
A zero records an empty place; it does not remove that place. In , there are no thousands and no tens. Keep both zeroes so the other digits stay in the correct columns.
| Ten-thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 4 | 0 | 2 | 0 | 6 |
Different ways to build the same number
Expanded form separates a number into its place values: . Read each part aloud, then add the parts to check that the number has stayed the same.
You can exchange one hundred for ten tens without changing the amount. For example, , so three hundreds and six tens can also be called thirty-six tens. This exchange explains how regrouping works in written calculations.
See the method in action.
Find a digit value
What is the value of 7 in 27,413?
Worked solution
- 1
Locate the thousands place.
Reading from the right puts the 7 in the thousands column.
- 2
Count the thousands represented by 7.
A digit tells how many units of its place are present.
- 3
State its value.
The value includes the place, rather than just the digit 7.
7,000.
Rename a number
Write 2,340 as hundreds, tens and ones, without using thousands.
Worked solution
- 1
Exchange the two thousands for hundreds.
Each thousand contains ten hundreds.
- 2
Combine all the hundreds.
The number already has three hundreds as well as the exchanged hundreds.
- 3
Keep the tens and ones and rebuild the number.
Twenty-three hundreds, four tens and zero ones have the original total value.
23 hundreds, 4 tens and 0 ones.
Try it yourself.
Check your understanding
In 50,407, what is the value of 4?
Show answer & reasoning
400.
In , the counts hundreds: . The zero in the tens column keeps the in the ones column.
Keep practising
6 worksheet questions · 8 marks
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 . 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: .
8,000. - Write 7,064 in expanded form.1 mark
The digits mean 7 thousands, 0 hundreds, 6 tens and 4 ones.
. - Build a number from 3 ten-thousands, 2 thousands, 5 hundreds, 0 tens and 9 ones.1 mark
.
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.
.
41 hundreds, 2 tens and 0 ones. - A learner writes 20,306 as . 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: .
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 ↗