Dividing Decimals Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Dividing Decimals.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Dividing numbers that contain decimal points, typically by converting the divisor to a whole number (multiplying both divisor and dividend by a power of 10) and then performing long division.

If you want to split $7.20 equally among 3 people, you're dividing a decimal. The trick for harder problems is: if the divisor is 0.40.4, multiply both numbers by 10 to get 72÷4=1872 \div 4 = 18. You haven't changed the answer—just made it easier to compute.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Dividing decimals multiplies both numbers by the same power of 10 so the divisor becomes a whole number, then does ordinary long division.

Common stuck point: The procedure for dividing decimals is the easy part; the trap is shifting only one number's point. Asking "Is the divisor a decimal I should make whole by shifting both points equally?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Is the divisor a decimal I should make whole by shifting both points equally?

Worked Examples

Example 1

easy
Calculate 3.6÷43.6 \div 4.

Answer

0.9

First step

1
Think: 36÷4=936 \div 4 = 9.

Full solution

  1. 2
    Since 3.6=36×0.13.6 = 36 \times 0.1, we get 3.6÷4=0.93.6 \div 4 = 0.9.
  2. 3
    Or: 4×0.9=3.64 \times 0.9 = 3.6 ✓.
Divide as whole numbers (36÷4=936 \div 4 = 9), then adjust the decimal: 3.6÷4=0.93.6 \div 4 = 0.9.

Example 2

medium
Calculate 5.4÷0.65.4 \div 0.6.

Example 3

medium
A jug holds 2.42.4 L of juice. Each cup holds 0.30.3 L. How many cups does the jug fill?

Example 4

hard
Why does 0.4÷0.2=20.4 \div 0.2 = 2 but 0.4÷2=0.20.4 \div 2 = 0.2? Explain the difference.

Example 5

challenge
Without long division, estimate 7.83÷0.397.83 \div 0.39 to one significant figure, then compute exactly.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Calculate 2.8÷42.8 \div 4.

Example 2

medium
Calculate 7.2÷0.97.2 \div 0.9.

Example 3

easy
Divide: 0.6÷30.6 \div 3.

Example 4

easy
Divide: 0.8÷20.8 \div 2.

Example 5

easy
Divide: 4.5÷54.5 \div 5.

Example 6

easy
Divide: 7.2÷37.2 \div 3.

Example 7

easy
Divide: 0.9÷30.9 \div 3.

Example 8

easy
Divide: 6.0÷46.0 \div 4.

Example 9

easy
Divide: 0.6÷0.20.6 \div 0.2.

Example 10

easy
Divide: 1.0÷41.0 \div 4.

Example 11

medium
Divide: 7.2÷0.47.2 \div 0.4.

Example 12

medium
Divide: 9.45÷0.59.45 \div 0.5.

Example 13

medium
Divide: 3.6÷0.043.6 \div 0.04.

Example 14

medium
Split $7.20\$7.20 equally among 33 people. How much each?

Example 15

medium
Divide: 5÷0.255 \div 0.25.

Example 16

medium
Divide and round to hundredths: 1÷31 \div 3.

Example 17

medium
Divide: 12.6÷0.612.6 \div 0.6.

Example 18

medium
A ribbon 4.54.5 m long is cut into 0.90.9 m pieces. How many pieces?

Example 19

medium
Divide: 8.4÷0.78.4 \div 0.7.

Example 20

challenge
A car travels 148.5148.5 km on 13.513.5 L. What is its fuel efficiency in km per L?

Example 21

challenge
Divide 2.5÷0.042.5 \div 0.04, then divide that result by 55. Give the final value.

Example 22

challenge
Find xx if 0.3x=1.50.3x = 1.5, using division. Then check by multiplying.

Example 23

easy
Divide: 0.8÷40.8 \div 4.

Example 24

easy
Divide: 0.5÷50.5 \div 5.

Example 25

easy
Divide: 2.4÷62.4 \div 6.

Example 26

easy
Divide: 3.6÷93.6 \div 9.

Example 27

easy
Divide: 1.2÷0.31.2 \div 0.3.

Example 28

easy
Divide: 4.8÷84.8 \div 8.

Example 29

easy
Divide: 0.36÷60.36 \div 6.

Example 30

medium
Divide: 6.25÷0.56.25 \div 0.5.

Example 31

medium
Divide: 0.84÷0.070.84 \div 0.07.

Example 32

medium
Divide: 15.75÷0.2515.75 \div 0.25.

Example 33

medium
A snack pack costs $1.20\$1.20. How many can you buy with $9.60\$9.60?

Example 34

medium
Divide: 4.5÷0.154.5 \div 0.15.

Example 35

medium
Divide and round to two decimal places: 5.0÷75.0 \div 7.

Example 36

medium
Divide: 0.144÷0.0120.144 \div 0.012.

Example 37

medium
A printer prints at 0.40.4 pages per second. How long does it take to print 5050 pages?

Example 38

hard
Divide: 0.625÷0.1250.625 \div 0.125.

Example 39

hard
A board is 2.342.34 m long and must be cut into pieces 0.130.13 m long. How many full pieces, and is there leftover?

Example 40

hard
Divide: 3.78÷1.53.78 \div 1.5.

Example 41

hard
A runner covers 42.19542.195 km in 2.52.5 hours. What is the average speed, in km/h?

Example 42

hard
Solve for xx: 0.04x=1.60.04 x = 1.6. Verify by multiplication.

Example 43

challenge
A recipe scales by dividing each ingredient by 0.750.75. If the original uses 1.51.5 cups of flour, how much should the scaled version use?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

divisionlong divisionplace value