Counting with zeros
You learn to work with numbers that end in zeros: leave the zeros off for a moment, then put them back.
How to work it out
- Count the zeros on the end of the numbers.
- Take them off and work with the small numbers.
- Put the same number of zeros back on the end.
- When you divide, take the same zeros off both numbers.
A worked example
5600 + 800
- Look at the zeros: both numbers end in two zeros.
- Take them off: 56 + 8.
- Work it out: 56 + 8 = 64.
- Put the 2 zeros back: 6400.
More examples
40 × 30
- Take off the 2 zeros: 4 × 3.
- Multiply: 4 × 3 = 12.
- Put the 2 zeros back: 1200.
2800 ÷ 4
- Take off the 2 zeros: 28 ÷ 4.
- Use the times table: 28 ÷ 4 = 7.
- Put the 2 zeros back: 700.
34 × 100
- 100 has 2 zeros.
- Put 2 zeros on the end of 34: 34 × 100 = 3400.
Try it yourself
3900 + 400 =
4500 + 4500 =
Watch out
You put back only one 0 when you took two off: for 40 × 30 you say 120.
Count the zeros you take off, and put exactly that many back.
You take more zeros off one number than the other: for 5600 + 800 you work out 56 + 80.
Take exactly the same zeros off both, or the places will not line up any more.
Tips
- When you divide by 10, 100 or 1000, zeros come off: 4500 ÷ 100 = 45.
- Check with multiplication: 7 × 4 = 28, so 700 × 4 = 2800.
Exceptions
- If the times table fact already ends in 0, like 5 × 6 = 30, still add the zeros: 5 × 600 = 3000.
- When you divide by a number with zeros, like 120 ÷ 40, take the same zeros off both: 12 ÷ 4 = 3.
Why it works
In 5600 + 800 both numbers end in zeros. Take two zeros off each and you are left with 56 + 8, a sum you know. Because you took the same zeros off both, you can simply put them back afterwards. When you multiply by 10, 100 or 1000, each digit moves one, two or three places to the left. Dividing does exactly the opposite.