The idea, step by step
The place gives the value
The digit 4 can mean four ones, four tens or four thousands. Its position tells us which. In 24,581 the 4 is worth 4,000, while the 5 is worth 500.
Each place is ten times the place on its right. Ten ones make one ten; ten tens make one hundred; ten hundreds make one thousand.
Use a place-value chart
A place-value chart keeps the digits lined up. For 30,406, use 3 ten-thousands, 0 thousands, 4 hundreds, 0 tens and 6 ones.
Regrouping changes the way we describe the amount, not the amount itself. Twelve thousands can be renamed as one ten-thousand and two thousands.
| Ten-thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 3 | 0 | 4 | 0 | 6 |
A common trap
Saying that the 6 in 36,204 has a value of six.
Instead: Six is the digit. Its value is 6,000 because it is in the thousands place.
See the thinking
Find a digit value
What is the value of 7 in 27,640?
- Locate the 7 in the thousands column.
- Seven thousands means 7 × 1,000.
Regroup thousands
Rename 16 thousands using ten-thousands and thousands.
- Ten of the sixteen thousands make one ten-thousand.
- Six thousands remain.
- The number is still 16,000.
Check your understanding
In 52,309, which digit is in the hundreds place?
Show answer
3
From the right, the places are ones, tens, then hundreds.
Your turn
6 questions · Work at your own pace.
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.
40,000 + 2,000 + 60 + 1 = 42,061.
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 ↗