How to do decimal long division

Decimal division gets easier when you first turn the divisor into a whole number. Move both decimal points the same number of places, then continue with ordinary long division.

Try 12.6 ÷ 0.3 Open decimal division Back to column arithmetic
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See the move before you divide

Step diagram that highlights both decimal points, changes 12.6 ÷ 0.3 into 126 ÷ 3, and then divides to 42.
This diagram highlights both decimal points moving together before the ordinary division starts.

The key idea is that both decimal points move by the same amount before you divide.

What you will learn

See it in 3 steps

  1. Move the decimal point in the divisor until the divisor becomes a whole number.
  2. Move the decimal point in the dividend the same number of places.
  3. Divide the transformed equation in the usual written way.

Try one example: 12.6 ÷ 0.3

  1. Move the decimal point in 0.3 one place to the right. It becomes 3.
  2. Move the decimal point in 12.6 one place to the right too. It becomes 126.
  3. Now divide 126 by 3. The answer is 42.

The reason for the same move is simple: both numbers change together, so the quotient stays the same.

Common mistakes

Mistake diagram showing the divisor decimal point moving without moving the dividend decimal point too.
Wrong: only the divisor changes. Better: move both decimal points together.

If only one side moves, you change the problem instead of making the same quotient easier to read.

Try it now

Try 4.8 ÷ 3 Try 12.6 ÷ 0.3 Try 3.75 ÷ 1.5

Where to go next

Questions learners ask

Why do both decimal points move the same number of places?

Because multiplying both numbers by the same power of 10 does not change the quotient. It only makes the divisor easier to divide by.

What do I do after the decimal-point move?

After the divisor becomes a whole number, continue with ordinary long division on the transformed equation.

What if the divisor has one decimal place?

Move both decimal points one place to the right. Use the same number of moves for both numbers.

What should I do after this page?

Try the decimal division calculator with the same example first. Then compare it with whole-number long division or decimal multiplication.

See also