Dividing Decimals

Learn how to divide decimal numbers using place value understanding and the standard algorithm.

Intermediate25 minLesson
Printable worksheet

Definition

Dividing decimals follows the same process as dividing whole numbers, with careful attention to decimal point placement.
Key strategies:
  1. 1.Dividing by a whole number: Divide normally, then place the decimal point in the quotient directly above where it appears in the dividend.
  1. 2.Dividing by a decimal: Multiply both the divisor and dividend by a power of 10 to make the divisor a whole number, then divide.
12.63=4.28.40.4=844=21\frac{12.6}{3} = 4.2 \quad\quad \frac{8.4}{0.4} = \frac{84}{4} = 21

Try it now

What is 6.4÷26.4 \div 2?

Worked Examples

Calculate 12.48÷412.48 \div 4
1

Set up the division

Place 12.4812.48 under the division symbol with 44 outside → 4)12.48‾4 \overline{)12.48}
2

Divide the whole number part

12÷4=312 \div 4 = 3 → Write 33 above the 22
3

Place the decimal point

Put the decimal directly above where it appears in 12.4812.48 → 3.3.
4

Divide the tenths

4÷4=14 \div 4 = 1 → 3.13.1
5

Divide the hundredths

8÷4=28 \div 4 = 2 → 3.123.12

Common Mistakes

Forgetting to move the decimal point in the dividend when making the divisor whole

Why it's wrong: When you multiply the divisor by 10 (or 100), you must do the same to the dividend to keep the division equivalent.

Correct: 8.4÷0.48.4 \div 0.4: Multiply BOTH by 10 to get 84÷4=2184 \div 4 = 21

Placing the decimal point in the wrong position in the quotient

Why it's wrong: The decimal in the quotient must align directly above where it appears in the dividend.

Correct: In 12.48÷412.48 \div 4, place the decimal after the 33: 3.123.12, not 31.231.2 or 0.3120.312

Stopping the division too early when there is a remainder

Why it's wrong: If there is a remainder, add zeros after the decimal and continue dividing.

Correct: 7÷47 \div 4: Don't stop at 11 R33. Add zeros: 7.00÷4=1.757.00 \div 4 = 1.75

Thinking dividing by a decimal less than 1 makes the answer smaller

Why it's wrong: Dividing by a number less than 1 actually makes the answer larger. Think: how many 0.50.5s fit into 33? Six!

Correct: 3÷0.5=63 \div 0.5 = 6 (larger than 3, not smaller)

Interactive Visual

Long Division

12.48÷412.48 \div 4
1 is smaller than 4, so start with 12.

Step 1 of 13

Place Value Chart

Enter a number:

12.48
Tens
10
Ones
1
Tenths
0.1
Hundredths
0.01
1248

Expanded Form:

1 × 10 + 2 × 1 + 4 × 0.1 + 8 × 0.01

Click on any place value to highlight it and see its value.

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

15 problems
Problem 1 of 15
Easy
What is 6.4÷26.4 \div 2?

Why It Matters

Decimal division is essential in everyday life:
  • Shopping: Calculating unit prices (1.89 euros for 3 items = 0.63 euros each)
  • Cooking: Scaling recipes up or down (0.75 liters shared among 3 servings)
  • Finance: Splitting costs equally among friends
  • Science: Converting measurements and analyzing data
  • Sports: Calculating batting averages and other statistics
Without decimal division, we couldn't solve many practical problems involving precise measurements!

Real World Applications

Unit Price Calculation

Stores use decimal division to calculate the price per item or per unit weight.

Example:

A pack of 6 yogurts costs 4.50 euros. Each yogurt costs 4.50÷6=0.754.50 \div 6 = 0.75 euros.

1Try It Yourself

A 2.5 kg bag of apples costs 3.75 euros.

What is the price per kilogram?

Step 1: Write the mathematical expression

Divide total price by weight:

Splitting Costs

Friends often need to divide costs equally, including amounts with decimals.

Example:

A dinner bill of 87.50 euros split 5 ways: 87.50÷5=17.5087.50 \div 5 = 17.50 euros each.

2Try It Yourself

Four friends share a taxi fare of 23.60 euros equally.

How much does each person pay?

Step 1: Write the mathematical expression

Divide the fare by the number of friends:

Key Takeaways

  • 1To divide by a whole number, divide normally and place the decimal point in the quotient directly above where it appears in the dividend
  • 2To divide by a decimal, multiply both the divisor and dividend by 10, 100, etc. to make the divisor a whole number
  • 3Add zeros after the decimal point if needed to continue dividing when there is a remainder
  • 4Dividing by a number less than 1 gives a quotient larger than the dividend

Frequently Asked Questions

Multiplying the numerator and denominator of a fraction by the same number keeps the value the same. 8.40.4=844\frac{8.4}{0.4} = \frac{84}{4} because both top and bottom were multiplied by 10.
Multiplying the numerator and denominator of a fraction by the same number keeps the value the same. 8.40.4=844\frac{8.4}{0.4} = \frac{84}{4} because both top and bottom were multiplied by 10.
Stop when: (1) there is no remainder, (2) you reach a repeating pattern, or (3) you have enough decimal places for your purpose (often 2 for money).
Think of it as: 'How many halves fit into 3?' Six halves make 3 wholes. Dividing by a fraction or decimal less than 1 asks how many small pieces fit into the whole.

Glossary

Dividend
The number being divided (the number inside or under the division symbol)
Divisor
The number you are dividing by (the number outside the division symbol)
Quotient
The result of a division
Remainder
The amount left over when a division does not come out evenly

Formula Card

Dividing by a whole number

a.bc÷na.bc \div n

Place decimal in quotient directly above decimal in dividend

Dividing by a decimal

a0.b=a×10b\frac{a}{0.b} = \frac{a \times 10}{b}

Multiply both numbers by $10^n$ to make divisor whole, then divide

Today's challengeOne problem, three tries

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