Dividing Decimals- Examples and Practice Problems

What Dividing Decimals Actually Means

Division with decimals isn't some special math operation. It's just division. The decimal point is the only thing that makes people freeze up.

When you divide 6 by 2, you get 3. When you divide 0.6 by 0.2, you still get 3. The numbers are smaller, but the relationship is the same.

The trick is making the divisor a whole number first. Move the decimal point, do the division, and put the decimal point in the answer where it belongs. That's it.

The Basic Method: Move the Decimal, Then Divide

Here's the step-by-step process that works every time:

Write your division problem
Move the decimal in the divisor to the right until it becomes a whole number
Move the decimal in the dividend the same number of places
Divide normally
Place the decimal point in your answer directly above where it appears in the dividend

That last step trips people up constantly. The decimal in your answer lines up with the decimal in the number you're dividing.

Simple Examples Step by Step

Example 1: 4.5 ÷ 0.5

The divisor is 0.5. Move the decimal one place to get 5.

Move the decimal in 4.5 the same way—one place to the right. You get 45.

Now divide 45 by 5.

45 ÷ 5 = 9

Answer: 9

You can verify this: 0.5 × 9 = 4.5 ✓

Example 2: 7.28 ÷ 0.7

Move the decimal in 0.7 one place to get 7.

Move the decimal in 7.28 one place to get 72.8.

Divide 72.8 by 7.

7 goes into 72 about 10 times (70), remainder 2. Bring down the 8 to get 28.

7 goes into 28 exactly 4 times.

Answer: 10.4

Example 3: 15 ÷ 0.25

Move the decimal in 0.25 two places to get 25.

Move the decimal in 15 two places. But 15 has no decimal point. Add a decimal and two zeros: 1500.

Divide 1500 by 25.

25 × 60 = 1500

Answer: 60

This makes intuitive sense. A quarter goes into a dollar four times. Four quarters go into 15 dollars 60 times.

Example 4: 0.144 ÷ 1.2

Move the decimal in 1.2 one place to get 12.

Move the decimal in 0.144 one place to get 1.44.

Divide 1.44 by 12.

12 doesn't go into 1, so start with 0. Then 12 goes into 14 once (12), remainder 2. Bring down the 4 to get 24.

12 goes into 24 exactly twice.

Answer: 0.12

Dividing Decimals by Whole Numbers

This is easier. You only move one decimal point—the one in the dividend.

Example: 8.64 ÷ 6

Just set up the problem and divide normally.

6 goes into 8 once (6), remainder 2. Bring down the 6 to get 26. 6 goes into 26 four times (24), remainder 2. Bring down the 4 to get 24. 6 goes into 24 exactly four times.

Place the decimal point in the answer directly above the decimal in 8.64.

Answer: 1.44

Dividing When the Dividend Is Smaller

When the number you're dividing is smaller than what you're dividing by, your answer starts with zero.

Example: 2.5 ÷ 8

8 doesn't go into 2. Write 0. and then keep working.

2.5 becomes 25 (after accounting for the decimal). 8 goes into 25 three times (24), remainder 1. Bring down nothing—add a zero to get 10. 8 goes into 10 once (8), remainder 2. Add another zero to get 20. 8 goes into 20 twice (16), remainder 4. Add another zero to get 40. 8 goes into 40 five times (40), remainder 0.

Answer: 0.3125

You can stop when the remainder hits zero, or when you have enough decimal places for your purposes.

Common Mistakes and How to Avoid Them

Most errors with decimal division come from a few predictable places:

Mistake	What Actually Happens
Forgetting to move the decimal in both numbers	The answer will be off by a factor of 10
Misplacing the decimal in the final answer	The answer will be completely wrong
Not moving the decimal far enough in the divisor	You're still dividing by a decimal—much harder
Dropping trailing zeros when they matter	0.5 and 0.50 are equal, but 0.5 ÷ 0.2 needs the decimal moved correctly

The fix is simple: always check your work by multiplying the answer by the divisor. You should get the dividend back. If you don't, something went wrong.

Quick Reference: Decimal Division Rules

Divisor has one decimal place? Move it one place. Dividend follows.
Divisor has two decimal places? Move it two places. Dividend follows.
Divisor is a whole number? Don't touch it. Just divide.
Dividend is smaller than divisor? Your answer starts with 0.
Never divide by a decimal if you can avoid it—convert it to a whole number first.

Practice Problems

Try these. The answers are below, but work through them first.

12.6 ÷ 0.3
5.5 ÷ 1.1
0.81 ÷ 0.09
48 ÷ 0.8
7.2 ÷ 9
0.156 ÷ 0.13
99 ÷ 0.25
2.464 ÷ 0.8

Answers

42 (0.3 × 42 = 12.6 ✓)
5 (1.1 × 5 = 5.5 ✓)
9 (0.09 × 9 = 0.81 ✓)
60 (0.8 × 60 = 48 ✓)
0.8 (9 × 0.8 = 7.2 ✓)
1.2 (0.13 × 1.2 = 0.156 ✓)
396 (0.25 × 396 = 99 ✓)
3.08 (0.8 × 3.08 = 2.464 ✓)

How to Check Your Work Fast

Every division problem is secretly a multiplication problem. If A ÷ B = C, then B × C = A.

Multiply your answer by the divisor. If you get the original number back, you're correct. If you don't, find the error.

This takes three seconds and catches most mistakes before you submit anything.