Long Division with Decimals- Step-by-Step Instructions
Long Division with Decimals: The No-Nonsense Guide
Long division with decimals isn't hard. It's just long division with extra steps. Once you see the pattern, you'll wonder why anyone made it sound scary.
This guide cuts through the nonsense. You'll find step-by-step instructions, clear examples, and a comparison table to help you pick the right method for your problem.
What Is Long Division with Decimals?
Long division with decimals is a process for dividing numbers that contain decimal points. You break down the division step by step, tracking where the decimal lands in your answer.
The good news: the decimal point doesn't change the division process. It only affects where you place the point in your final answer.
Dividing Decimals by Whole Numbers
This is the easiest case. The whole number stays as-is; you just need to place the decimal correctly.
Step-by-Step Process
- Write the division problem with the decimal inside the division bracket
- Position the decimal point in the answer area, directly above the decimal in the dividend
- Divide as you normally would with whole numbers
- Bring down digits and continue until you have no remainder or reach your desired decimal places
Example
Let's divide 15.75 ÷ 3
3 goes into 15 exactly 5 times. Write 5 above the 5.
3 goes into 7 twice, with 1 left over. Write 2 above the 7.
Bring down the 5 to get 15. 3 goes into 15 exactly 5 times.
The answer is 5.25. The decimal point sits right above where it was in the original number.
Dividing a Whole Number by a Decimal
When your divisor has a decimal, you need to move the decimal point first. This makes the divisor a whole number.
The Decimal Shift Trick
Count how many places the decimal moves. Then move the decimal in the dividend the same direction by the same amount.
Example: 8 ÷ 0.4
The divisor 0.4 needs to become 4. That's moving the decimal one place to the right.
Move the decimal in 8 one place right: 8 becomes 80.
Now solve 80 ÷ 4 = 20. That's your answer.
Dividing Decimals by Decimals
Combine both techniques. First, convert the divisor to a whole number. Then solve the new problem.
Example: 6.75 ÷ 0.45
The divisor is 0.45. Move the decimal two places right to get 45.
Move the decimal in 6.75 two places right: 6.75 becomes 675.
Now solve 675 ÷ 45.
45 goes into 67 once. Subtract 45, get 22.
Bring down the 5. 45 goes into 225 five times.
The answer is 15.
Getting the Right Number of Decimal Places
Sometimes the division doesn't come out even. You can keep going to get more decimal places in your answer.
Simply add zeros to the right of your dividend and continue dividing.
Example: 10 ÷ 4
4 goes into 10 twice, with 2 remaining.
Add a zero: bring down 0 to get 20.
4 goes into 20 five times. No remainder.
Answer: 2.5
Keep adding zeros if you need more precision.
Rounding Decimals in Division
Most problems ask for a specific number of decimal places. Round your final answer accordingly.
- Look at the digit after your last required place
- If it's 5 or higher, round up
- If it's 4 or lower, leave it as-is
Example: You need 2 decimal places and get 3.847
The third decimal place is 7, which is 5 or higher. Round the second decimal up from 4 to 5.
Your answer is 3.85
Where People Screw Up
Misplacing the decimal point. This is the most common mistake. Always place the answer's decimal directly above where it sits in the dividend.
Forgetting to shift both numbers. When converting the divisor to a whole number, you must shift the dividend by the same amount. Skipping this step gives you the wrong answer.
Dropping trailing zeros. Zeros at the end of a decimal matter. 0.5 and 0.50 are the same value, but when adding zeros for continued division, don't drop them mid-calculation.
Quick Reference Table
| Problem Type | First Step | Then Do |
|---|---|---|
| Decimal ÷ Whole Number | Place decimal in answer | Divide normally |
| Whole Number ÷ Decimal | Convert divisor to whole number | Divide normally |
| Decimal ÷ Decimal | Convert divisor to whole number | Convert dividend same way |
| Uneven result | Add zeros to dividend | Continue dividing |
Practice Problems
Try these to test yourself:
- 12.6 ÷ 3 = ?
- 7 ÷ 0.5 = ?
- 4.5 ÷ 0.25 = ?
- 15 ÷ 8 (round to 2 decimal places)
Answers:
- 4.2
- 14
- 18
- 1.88
The Bottom Line
Long division with decimals follows the same process as regular long division. The only difference is tracking the decimal point and knowing when to shift it.
Convert the divisor to a whole number first. Move the decimal in your dividend the same amount. Then divide normally. Place your decimal point directly above its position in the original dividend.
Practice three or four problems and it'll click. That's it.