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Multiplying and Dividing Decimals by 10, 100 and 1,000

Level 1 Decimals · Reviewed by The NumThink editorial team · Last reviewed

Short version: Count the zeros and move the decimal point that many places: right to multiply (3.7 × 10 = 37), left to divide (4.5 ÷ 10 = 0.45).

This page is part of the NumThink Decimals course. Read why the method works, watch it run on worked examples, then drill it in the practice box below until it feels automatic.

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Why it works

Each place is worth 10 times the place to its right. Multiplying by 10 makes every digit worth 10 times more, so each digit moves one place to the left — which looks exactly like the decimal point moving one place to the right: 3.7 × 10 = 37.

Dividing by 10 does the opposite: every digit becomes worth a tenth as much, so the point moves one place to the left: 4.5 ÷ 10 = 0.45. Count the zeros in 10, 100 or 1,000 to know how many places to move.

The steps

  1. Count the zeros. ×100 or ÷100: two zeros, so two places.
  2. Move the point: right to multiply, left to divide. 2.35 × 100 → 235, and 2.35 ÷ 100 → 0.0235.
  3. Fill empty places with zeros. 4.5 × 100: 4.5 → 45 → 450.

Worked examples

Easy 3.7 × 10

Show the thinking

One zero: move the point one place right

3.7 → 37

So 3.7 × 10 = 37.

Answer: 37

Medium 4.5 × 100

Show the thinking

Two zeros: move the point two places right

4.5 → 45 → 450 (the empty place becomes 0)

So 4.5 × 100 = 450.

Answer: 450

Hard 6.2 ÷ 1,000

Show the thinking

Three zeros: move the point three places left

6.2 → 0.62 → 0.062 → 0.0062

So 6.2 ÷ 1,000 = 0.0062.

Answer: 0.0062

When to use it

  • Converting units: 3.5 m is 350 cm (×100), and 750 g is 0.75 kg (÷1,000).
  • Prices: 10 items at 2.45 each cost 24.5 (×10).

When NOT to use it

  • Multiplying by numbers that are not 10, 100 or 1,000: split them — 3.2 × 20 = 3.2 × 2 × 10 = 64.
  • Whole numbers ending in zeros: just remove or add zeros (250 ÷ 10 = 25). Other whole numbers have a hidden point at the end: 253 ÷ 10 = 25.3.

Common mistakes

Adding a zero after the point. Writing 3.7 × 10 = 3.70. Fix: 3.70 is still the same number as 3.7. Move the point instead: 37.
Moving the point the wrong way. Writing 4.5 ÷ 10 = 45. Fix: Dividing makes the number smaller, so the point moves left: 0.45.
Check yourself: Check the size: ×10 must make a number bigger and ÷10 smaller. 0.45 is smaller than 4.5 ✓.