Long Division with Decimals: Step-by-Step Guide

When you do long division and there's a remainder left over, you don't have to stop there. Instead of writing R3 at the end, you can keep going and turn that remainder into decimal digits. This is long division with decimals — the same method you already know, extended past the ones place.

This guide covers two things: how to continue a division problem past a remainder to get a decimal answer, and how to divide a number that already has a decimal point in it. If you need a refresher on the core method first, see our guide to how to do long division.

The Key Idea: What a Remainder Really Is

A remainder is just what's left when a number doesn't divide evenly. When you divide 7 by 4, you get 1 remainder 3. That remainder of 3 means the division isn't finished — there's still 3 left to share.

In whole number division, you stop and write the remainder. In decimal division, you keep going. The trick is simple: when you run out of digits to bring down, place a decimal point in the quotient and attach a zero to the remainder. Then divide again. Repeat until the remainder is zero (or until you have enough decimal places for your purposes).

How to Do Long Division with Decimals: Step by Step

Here's the full process for 7 ÷ 4 — including what the scratch work looks like on paper:

The remainder reached zero, so the answer is exact. Check: 1.75 × 4 = 7 ✓

Dividing a Whole Number That Doesn't Divide Evenly

The same process applies whenever a division produces a remainder. Here's 9 ÷ 2:

How to Divide a Decimal by a Whole Number

Sometimes the dividend already has a decimal point — for example, dividing 8.4 by 3, or splitting a 7.5-metre rope into 5 equal pieces. The method is the same as regular long division. The only rule: when you reach the decimal point in the dividend, write a decimal point in the quotient directly above it, then keep going.

Check: 2.8 × 3 = 8.4 ✓

A Longer Example: Multiple Decimal Places

Some divisions take more steps before the remainder reaches zero. Here's 5 ÷ 8, which needs three decimal places:

Check: 0.625 × 8 = 5 ✓ Three decimal places were needed here, but the remainder still reached zero, so the answer is exact.

What Happens When the Remainder Never Reaches Zero

Not every division produces a neat decimal. 1 ÷ 3, for example, gives 0.333… — the 3s go on forever. This is called a repeating decimal (sometimes written as 0.3̄). You'll notice the same remainder keeps reappearing as you work through the steps.

In practice, stop when you have enough decimal places — usually 2 is plenty. For money, you'd round to the nearest cent. For a school problem, follow whatever instructions you're given.

For more on what remainders mean and how they work in whole-number division, see our guide to understanding remainders.

Checking Your Answer

The check is the same as for all division: multiply the quotient by the divisor. If you get back to the original dividend, you're right. This works even with multiple decimal places — if 5 ÷ 8 = 0.625, then 0.625 × 8 = 5. Getting into this habit catches errors early, especially a misplaced decimal point.

For more worked problems to practice with, our long division examples post walks through a range of cases including those that produce decimal answers.

Common Mistakes to Avoid

Forgetting the decimal point in the quotient. When you attach that first zero to the remainder, you must also place a decimal point in the quotient at the same moment. Skipping it shifts every digit that follows by a factor of 10.

Attaching the zero in the wrong place. The zero always attaches to the current remainder — remainder 3 becomes 30, not 03 or 300.

Stopping one step too early. If there's still a remainder after your last decimal digit, keep going. The remainder isn't gone just because you have a decimal point in the answer.