Multiplying and Dividing by 10, 100 and 1000
Solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits.
Read this first
The digits move. They do not change.
Multiply by 10 and every digit moves one column left.
Words you need
- Column
- Each spot a digit sits in. Ones, tens, hundreds, thousands.
- Multiply
- Make bigger by making equal groups.
- Divide
- Share into equal groups.
Worked example
e.g. What is 36 x 10?
- Write 36 in columns. The 3 is in the tens. The 6 is in the ones.
- Times 10 makes each digit worth ten times more.
- Each digit moves one column left. A 0 fills the ones.
- 36 x 10 = 360.
Do not say you add a zero. Say the digits move left. That works for decimals too.
Practice
The pictures fade as you go. By the last few you are on your own.
1What is 52 x 10?with a picture
Answer520.
2What is 7 x 100?with a picture
Answer700. The 7 moves two columns left.
3What is 4 x 1000?with a hint
Need a hint?
The digit moves three columns left.
Answer4000.
4What is 800 divided by 10?with a hint
Need a hint?
Dividing moves digits to the right.
Answer80.
5What is 63 x 100?on your own
Answer6300.
6What is 5000 divided by 100?on your own
Answer50.
7What is 240 divided by 10?on your own
Answer24.
Think about it
1
Why is 'add a zero' a risky rule?
One good answerIt stops working with decimals. 0.4 x 10 is 4, not 0.40.
2
What happens to a digit when you divide by 100?
One good answerIt moves two columns to the right.
Common mistakes
Adding a zero to the end.
That only works for whole numbers. Think about columns instead.
The digits change.
They never change. Only the column they sit in changes.