Decimal Long Division Calculator – Step-by-Step Guide (2025)

What Is Decimal Long Division?

Decimal long division is the standard long-division process applied to numbers with decimals. You still repeat the cycle bring down → divide → multiply → subtract, but you must track the decimal point carefully.

Two Situations (and What to Do)

1) Dividing a decimal by a whole number

Place the decimal in the quotient directly above the decimal in the dividend, then divide as usual.

2) Dividing a decimal by a decimal

First make the divisor an integer by moving its decimal to the right. Move the dividend’s decimal by the same number of places, then divide normally.

Worked Example #1 — 12.48 ÷ 0.6

1. Make the divisor an integer: move 0.6 → 6 (one place). Move the dividend one place too: 12.48 → 124.8.
2. Now compute 124.8 ÷ 6 with long division.
3. 6 goes into 12 → 2 (remainder 0). Bring down 4 → 6 goes into 4 → 0 (remainder 4). Bring down 8 → 6 goes into 48 → 8.
4. Track the decimal: 124.8 had one decimal place; in the quotient place the decimal directly above that position.

Answer: 12.48 ÷ 0.6 = 20.8

Worked Example #2 — 5 ÷ 10

This is a friendly starter: dividing by ten shifts the decimal one place left.

• Write 5 as 5.0
• Divide by 10 → move decimal one place left → 0.5

Answer: 5 ÷ 10 = 0.5

Worked Example #3 — 230 ÷ 9 (Repeating)

1. Integer part: 9 goes into 230 → 25 remainder 5.
2. Add a decimal and zeros to continue: bring down 0 → 50 ÷ 9 → 5 remainder 5 → bring down 0 → 50 ÷ 9 → repeats.

Answer: 230 ÷ 9 = 25.5(5) where the 5 repeats.

Step-by-Step Rules (Quick Reference)

1. Line up the place values. If the divisor has a decimal, shift both numbers right the same number of places to make the divisor an integer.
2. Divide as usual. Repeat divide → multiply → subtract → bring down.
3. Place the decimal. In the quotient, place it directly above where it falls in the (shifted) dividend.
4. Extend with zeros. If the digits run out and you still have a remainder, add zeros after the decimal and continue.
5. Stop or mark a repeat. Stop if the remainder hits 0; otherwise, identify repeating digits and write them with parentheses.

Common Mistakes (and Fixes)

• Forgetting to shift the dividend when you clear the divisor’s decimal. Shift both by the same count.
• Placing the decimal late. Put the decimal in the quotient as soon as you reach the decimal point position.
• Stopping too early. If your teacher wants decimals, keep adding zeros until the required number of places.
• Not recognizing repeats. Watch for the same remainder cycling back — that means a repeating decimal.

FAQ: Decimal Long Division Calculator

How do I divide a decimal by a whole number?

Place the decimal in the answer directly above the decimal in the dividend, then divide normally. Extend with zeros if needed.

What do I do if the divisor is also a decimal?

Move the decimal right in the divisor until it becomes an integer, and move the dividend’s decimal right by the same number of places. Then divide as usual.

Where does the decimal go in the quotient?

Directly above the decimal position in the (possibly shifted) dividend. If you cleared the divisor’s decimal, use the shifted dividend to determine the position.

How do I show repeating decimals?

When a remainder repeats, the same block of digits will repeat. Write the repeating block in parentheses, for example 0.(3) or 1.2(54).

Can I do this with negative decimals?

Yes. Divide the absolute values using the same method. Apply the sign at the end: negative if the inputs have opposite signs, positive if they match.