Multiplying by 10 makes every digit ten times bigger, so each digit moves one place to the left. Multiplying by 100 moves digits two places, and by 1000 three places. Dividing moves the digits to the right. The decimal point stays still; use zeros to fill empty places. Adding a zero on the end only works for whole numbers.
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
- place value
- the value a digit has because of where it is
- power of ten
- 10, 100, 1000 and so on
Worked examples
45 × 100 = ?
- 1.× 100 moves each digit two places to the left.
- 2.45 becomes 4500.
= 4500
3.7 × 100 = ?
- 1.× 100 moves each digit two places to the left.
- 2.The 3 moves to the hundreds and the 7 to the tens: 370.
= 370
4.2 × ? = 4200
- 1.The 4 moved from the ones to the thousands: three places left.
- 2.Three places left means × 1000.
= 1000
For parents
Method: Move the digits
What to say: Should the answer be bigger or smaller? How many places do the digits move?
Common mistakes:
- Moves the digits the wrong way: makes the number smaller when multiplying (or bigger when dividing), or does the same operation again to find a missing start.
- Moves the digits the wrong number of places (for example one or three places for × 100).
- Multiplies a decimal by 10, 100 or 1000 by writing zeros on the end ('just add a zero').
- Finds a missing power of ten by counting the zeros in the whole number, ignoring the decimal places of the other number.
- Finds the difference between the two numbers instead of the power of ten that links them.