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Decimals × and ÷ 10, 100, 1000

You learn to multiply and divide decimals by 10, 100 and 1000 by moving the decimal point.

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How to work it out

  1. Count the zeros: 10 has 1, 100 has 2, 1000 has 3.
  2. Move the decimal point that many places: right to multiply, left to divide.
  3. Fill any empty places with a 0.
D1.000
—
H100
—
T10
—
E1
3
t0,1
4
h0,01
5
3 + 0,4 + 0,05=345

A worked example

3.4 × 100

  1. 100 has 2 zeros.
  2. Move the decimal point 2 places to the right.
  3. There is only one digit after the decimal point, so fill the gap with a 0.
  4. So 3.4 × 100 = 340.
D1.000
—
H100
0
T10
3
E1
4
30 + 4=034
More examples

45 ÷ 100

  1. 100 has 2 zeros: move the decimal point 2 places to the left.
  2. Put a 0 in front of the decimal point: 45 ÷ 100 = 0.45.
D1.000
—
H100
0
T10
4
E1
5
40 + 5=045

0.25 × 10

  1. 10 has one 0: move the decimal point 1 place to the right.
  2. So 0.25 × 10 = 2.5.
D1.000
—
H100
0
T10
2
E1
5
20 + 5=025

Try it yourself

  1. 3.4 × 100 =

  2. 0.12 × 100 =

Watch out

  • You put zeros on the end of the decimal: 3.4 × 100 becomes 3.400.

    A 0 on the end of a decimal changes nothing. Move the decimal point itself to the right.

  • You move the decimal point the wrong way: 45 ÷ 100 becomes 4500.

    Dividing makes the number smaller, so the decimal point moves to the left.

Tips

  • When you multiply, the decimal point moves right; when you divide, it moves left.
  • The number of zeros is the number of places the decimal point moves.

Why it works

Times 10 makes every digit worth ten times as much: tenths become ones. That is the same as moving the decimal point one place to the right. When you divide, it moves to the left, and you fill any empty places with a 0.