Understand the idea.
The place gives the value
A digit tells how many; its place value tells what kind of units are counted. In , the counts thousands, so its value is . The counts hundreds, so it is worth .
Moving one place to the left makes a unit ten times as large. Ten ones make one ten, ten tens make one hundred, and ten hundreds make one thousand. This is why exchanging between neighbouring places works.
Use a place-value chart
Use the chart to read every place in . A zero records no units of that place: there are no thousands or tens. Skipping those columns would move other digits and change the number.
Regrouping describes the same amount using different units. Twelve thousands can be split into ten thousands and two thousands. Exchange the group of ten for one ten-thousand; nothing has been added or removed.
| Ten-thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 3 | 0 | 4 | 0 | 6 |
See the method in action.
Find a digit value
What is the value of 7 in 27,640?
Worked solution
- 1
Find the place occupied by seven.
Counting from the right gives ones, tens, hundreds, then thousands; seven is in the thousands place.
- 2
Find the value of seven thousands.
Each of the seven units is one thousand.
7,000
Regroup thousands
Rename 16 thousands using ten-thousands and thousands.
Worked solution
- 1
Separate a group of ten thousands.
Sixteen thousands contain ten thousands with six thousands left.
- 2
Exchange the group of ten.
Ten thousands make one ten-thousand.
- 3
Keep the remaining six thousands.
The same amount is one ten-thousand and six thousands.
1 ten-thousand and 6 thousands.
Try it yourself.
Check your understanding
In 52,309, which digit is in the hundreds place?
Show answer & reasoning
3
In , count from the right: ones, tens, then hundreds. The requested digit is , rather than its value of .
Keep practising
6 worksheet questions
Read the questions online
- What is the value of 8 in 18,432?
- What is the value of 8 in 42,815?
- Which digit is in the tens place in 26,307?
- Write the number with 4 ten-thousands, 2 thousands, 0 hundreds, 6 tens and 1 one.
- Rename 23 thousands using ten-thousands and thousands.
- In 45,154, compare the values of the two digits 4.
Read the worked solutions
- What is the value of 8 in 18,432?
The 8 is in the thousands place.
8,000 - What is the value of 8 in 42,815?
The 8 is in the hundreds place.
800 - Which digit is in the tens place in 26,307?
The final three digits are 307: 3 hundreds, 0 tens, 7 ones.
0 - Write the number with 4 ten-thousands, 2 thousands, 0 hundreds, 6 tens and 1 one.
.
42,061 - Rename 23 thousands using ten-thousands and thousands.
20 thousands make 2 ten-thousands; 3 thousands remain.
2 ten-thousands and 3 thousands. - In 45,154, compare the values of the two digits 4.
The left 4 is in the ten-thousands place. The final 4 is in the ones place.
The left 4 is worth 40,000; the right 4 is worth 4.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Numbers beyond 10,000; place value; ordering; estimating quantities and answers.
Official curriculum source ↗