Big numbers are grouped in threes: ones, thousands, millions. Each column is worth ten times the column to its right. A digit's value is the digit times its column: in 4 725 316 the 7 is in the hundred thousands, so it is worth 700 000. The digits after it are replaced by zeros. To add 10 000, change the ten thousands digit; if it is 9, it becomes 0 and the next column goes up by one.
Explore this idea with maths tools
Build a number
2 tens + 4 ones = 20 + 4 = 24
Move from 29 to 30. Ten ones become one ten. The amount stays the same when you regroup.
Words to know
- value
- what a digit is worth in its column
- expanded form
- a number written as the sum of its digits' values
- million
- one thousand thousands: 1 000 000
Worked examples
What is the value of the digit 7 in 4 725 316?
- 1.The 7 is in the hundred thousands column.
- 2.7 × 100 000 = 700 000.
= 700000
4 205 307 = 4 000 000 + ? + 5000 + 300 + 7
- 1.The missing part is the 2 in the hundred thousands column.
- 2.2 × 100 000 = 200 000.
= 200000
What is 10 000 more than 2 995 314?
- 1.The ten thousands digit is 9. Adding 1 makes 10: write 0 and carry 1.
- 2.The hundred thousands go from 9 to 10 as well, so the millions go up: 3 005 314.
= 3005314
For parents
Method: Place value chart
What to say: Which column is the digit in? What is that column worth?
Common mistakes:
- Gives the digit itself instead of its value (the 7 in 4 725 316 is 7).
- Counts the digit's own column as a zero, so the value has one zero too many.
- Gives the digit together with all the digits after it (the 7 in 4 725 316 is worth 725 316).
- Adds or subtracts in the column next to the right one (10 000 more changes the thousands).
- Changes the digit without exchanging with the next column (9 goes to 0 without a carry; 0 goes to 9 without a borrow).
- Subtracts when asked for 'more', or adds when asked for 'less'.