Multiplying and Dividing by 10, 100 and 1000

In short: Multiplying by 10, 100 or 1000 adds one, two or three zeros to a whole number, and dividing takes them away. For numbers that end in zeros, multiply the small parts first, then add all the zeros back.

Before you start

Times tables up to $12 \times 12$ .
Place value: in $4300$ the 4 means 4 thousands and the 3 means 3 hundreds.
$10 = 1 0^{1}$ , $100 = 1 0^{2}$ , $1000 = 1 0^{3}$ . These are called powers of ten.

Multiplying by 10, 100, 1000

Multiplying by tens, hundreds and thousands

Split the number into a small part and a power of ten.

Dividing with zeros

When you divide, you can cross off the same number of zeros from the end of both numbers. The answer does not change.

Estimating

To estimate, round each number to one that is easy, then multiply. The sign $\approx$ means "about equal to".

Estimates help you check answers. If your exact answer to $702 \times 19$ were $1338$ , the estimate of $14000$ tells you something went wrong.

Powers of ten

Multiply by 10, 100, 1000

Add 1, 2 or 3 zeros
Digits move left

Zeros on both

Small fact first
Then count all the zeros

Divide

Cross off the same zeros
$1210 \div 110 = 121 \div 11$

Estimate

Round to easy numbers
$702 \times 19 \approx 14000$

Quick summary

$\times 10$ adds one zero, $\times 100$ adds two, $\times 1000$ adds three.
For numbers ending in zeros, multiply the small parts and then add all the zeros.
Keep any zero that is part of the small fact, such as $5 \times 4 = 20$ .
To divide, cross off the same number of zeros from both numbers.
Estimate by rounding to easy numbers. Use $\approx$ for "about".

Quiz

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Try 3 questions now

$43 \times 1000 =$
1. A 4300
2. B 43 000
3. C 430 000
4. D 4 300 000
Show answer
B: 43 000
Times 1000 adds three zeros.
$48 \times 30 =$
1. A 144
2. B 1440
3. C 14 400
4. D 1200
Show answer
B: 1440
$48 \times 3 = 144$ , then add one zero.
$700 \times 800 =$
1. A 5600
2. B 56 000
3. C 560 000
4. D 5 600 000
Show answer
C: 560 000
$7 \times 8 = 56$ and there are 4 zeros.