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Multiply & divide by 10, 100, 1000

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The number system

Multiplying & dividing by 10, 100 and 1000

A dose of 10 ml is ten times bigger than 1 ml, and ten times smaller than 100 ml. Getting that right matters — and the digits do all the work for you.

Multiply → digits move LEFT (bigger)3.45× 100345Divide → digits move RIGHT (smaller)16.8÷ 101.6810 → 1 place100 → 2 places1000 → 3 places

Which way do the digits move?

• Multiplying makes a number BIGGER, so the digits move to the LEFT. • Dividing makes a number SMALLER, so the digits move to the RIGHT. How far they move depends on the number: • 10 → 1 place • 100 → 2 places • 1000 → 3 places

The digits move, not the point

It looks as though the decimal point jumps about — but it does not. The POINT stays where it is, and the DIGITS slide past it into new columns. That is why 3.45 × 100 = 345. The 3 slides from the ones column to the hundreds, the 4 from tenths to tens, and the 5 from hundredths to ones. Thinking of it this way stops you moving the point the wrong way.

Filling the gaps with zeros

Sometimes a digit moves into a column where there is nothing yet. Put a zero there to hold the place. 58 × 100 = 5800 — two zeros fill the tens and ones. 7 × 1000 = 7000 — three zeros. Those zeros are PLACE HOLDERS. Without them the digits would sit in the wrong columns and the number would be wrong.

Checking your answer

Ask yourself one question: should the answer be bigger or smaller than what I started with? × 10, × 100, × 1000 → the answer must be BIGGER. ÷ 10, ÷ 100, ÷ 1000 → the answer must be SMALLER. If 33 ÷ 10 gave you 330, you would know instantly that something has gone the wrong way.

Worked examples

Multiplying: 3.45 × 100

  1. Multiplying by 100 makes the number bigger, so the digits move two places LEFT.
  2. The 3 moves from ones to hundreds, the 4 from tenths to tens, the 5 from hundredths to ones.

Answer: 3.45 × 100 = 345

Dividing: 16.8 ÷ 10

  1. Dividing by 10 makes the number smaller, so the digits move one place RIGHT.
  2. The 1 moves from tens to ones, the 6 from ones to tenths, the 8 from tenths to hundredths.

Answer: 16.8 ÷ 10 = 1.68

Needing place holders: 456 × 1000

  1. Multiplying by 1000 moves the digits three places LEFT.
  2. That leaves the hundreds, tens and ones columns empty.
  3. Write a zero in each one to hold the place.

Answer: 456 × 1000 = 456 000

Working backwards: 2700 ÷ ▢ = 27

  1. The answer is smaller, so this is a division.
  2. 2700 became 27 — the digits moved two places RIGHT.
  3. Two places means dividing by 100.

Answer: 2700 ÷ 100 = 27

Three steps in a row

  1. Sofia multiplies a number by 10, then by 10 again, then by 10 again. Her answer is 20 000.
  2. Three multiplications by 10 is the same as one multiplication by 1000.
  3. So work backwards: 20 000 ÷ 1000.

Answer: She started with 20

Where you see this in real life

  • Changing centimetres to metres means dividing by 100 — 250 cm is 2.5 m.
  • Working out the cost of 100 identical items: multiply the price by 100.
  • Changing grams to kilograms means dividing by 1000 — 1500 g is 1.5 kg.

Key words

Digit
One of the symbols 0–9 used to write numbers.
Place value
The value of a digit because of its position in the number.
Decimal point
The dot that separates whole numbers from parts of a number.
Place holder
A zero written to keep the other digits in the right columns.
Tenth
The first place after the decimal point — one part out of ten.
Hundredth
The second place after the decimal point — one part out of a hundred.
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