Dividing Decimals
Grade 5 · Math · Study Guide
Master decimal division by whole numbers and by other decimals using clear step-by-step methods.
When dividing a decimal by a whole number, set up the division normally and bring the decimal point straight up into the quotient. Divide as usual, placing each digit of the quotient directly above the corresponding digit of the dividend.
When dividing by a decimal, multiply both the divisor and the dividend by a power of 10 to make the divisor a whole number first. For example, 1.6 ÷ 0.4 becomes 16 ÷ 4 = 4 by multiplying both by 10.
Adding zeros to the dividend lets you continue dividing until there is no remainder or the decimal terminates. Check answers by multiplying the quotient by the divisor — you should get back the dividend.
| Problem | Method | Answer |
|---|---|---|
| 3.6 ÷ 3 | Divide normally, bring decimal point up | 1.2 |
| 4.8 ÷ 6 | Divide normally, bring decimal point up | 0.8 |
| 7.5 ÷ 5 | Divide normally, bring decimal point up | 1.5 |
| Original Problem | Multiply Both By | New Problem | Answer |
|---|---|---|---|
| 2.4 ÷ 0.6 | × 10 | 24 ÷ 6 | 4 |
| 0.36 ÷ 0.9 | × 10 | 3.6 ÷ 9 | 0.4 |
| 1.5 ÷ 0.05 | × 100 | 150 ÷ 5 | 30 |
Key terms
- Dividend
- The number being divided in a division problem.
- Divisor
- The number you are dividing by.
- Quotient
- The answer to a division problem.
- Power of 10 Trick
- Multiply both dividend and divisor by the same power of 10 to eliminate the decimal in the divisor.
Practice questions
What is 6.4 ÷ 8?
- 8.0
- 0.8
- 80
- 0.08
Show answer
Answer: 0.8
Divide 6.4 by 8. 64 ÷ 8 = 8, then place decimal: 0.8.
What is 3.6 ÷ 0.9?
- 0.4
- 40
- 4
- 0.04
Show answer
Answer: 4
Multiply both by 10: 36 ÷ 9 = 4.
9.0 ÷ 5 = ___
Show answer
Answer: 1.8
90 ÷ 5 = 18, one decimal place → 1.8.
0.48 ÷ 0.6 = ___
Show answer
Answer: 0.8
Multiply both by 10: 4.8 ÷ 6 = 0.8.
A ribbon is 4.5 meters long. It is cut into pieces that are each 0.5 meters. How many pieces are there?
- 9
- 0.9
- 90
- 0.09
Show answer
Answer: 9
4.5 ÷ 0.5: multiply both by 10 → 45 ÷ 5 = 9 pieces.
Fun facts
- When you split a restaurant bill, you are dividing a decimal — $37.80 ÷ 3 people = $12.60 each!
- Computers use binary decimal division millions of times per second to run every program you use.
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