Dividing Decimals

Learn how to divide decimal numbers step by step.

beginnerdecimalsdivisionUpdated 2026-02-02

For Elementary Students

Dividing a Decimal by a Whole Number

This is the easiest type! Just divide like normal and put the decimal point in the answer right above where it is in the problem.

Think about it like this: The decimal point goes straight up — like an elevator!

Example: 8.4 ÷ 4 = ?

Step 1: Set up like regular division


   ---
4 | 8.4

Step 2: Divide 8 by 4 = 2

Step 3: Put the decimal point in the answer (right above the one in 8.4!)

    2.
   ----
4 | 8.4
    8
    0

Step 4: Bring down the 4 and divide

4 ÷ 4 = 1

Answer: 8.4 ÷ 4 = 2.1

Another Example: 15.6 ÷ 3

3 into 15 = 5
Put decimal point straight up
3 into 6 = 2

Answer: 5.2

Dividing by a Decimal: Make It a Whole Number!

When you're dividing by a decimal, you need to make it a whole number first!

The trick: Move the decimal point to the right until the divisor is a whole number. Then move the decimal in the dividend the same number of places!

Example: 7.2 ÷ 0.3 = ?

Step 1: The divisor is 0.3 (a decimal). Move the decimal 1 place right → 3

Step 2: Move the decimal in 7.2 the same amount (1 place right) → 72

Step 3: Now divide: 72 ÷ 3 = 24

Answer: 24

Memory trick: Whatever you do to one side, do to the other!

Quick Trick: Dividing by 10, 100, 1000

Super easy shortcut!

Divide by 10: Move the decimal point 1 place left

45.3 ÷ 10 = 4.53

Divide by 100: Move it 2 places left

45.3 ÷ 100 = 0.453

Divide by 1000: Move it 3 places left

45.3 ÷ 1000 = 0.0453

Memory trick: Dividing makes numbers smaller, so the decimal moves LEFT!

For Junior High Students

Dividing a Decimal by a Whole Number

This works just like long division. Place the decimal point in the answer directly above where it is in the dividend.

Key rule: The decimal point in the quotient (answer) goes directly above the decimal point in the dividend.

Example: 8.4 ÷ 4

Steps:

Divide: 4 into 8 = 2
Place the decimal point in the answer above the dividend's decimal
Bring down: 4 into 4 = 1

Answer: 2.1

Example: 15.6 ÷ 3

3 into 15 = 5
Decimal point goes up
3 into 6 = 2

Answer: 5.2

Dividing by a Decimal

When the divisor is a decimal, you need to make it a whole number first.

The Method:

Move the decimal point in the divisor to the right until it's a whole number
Move the decimal point in the dividend the same number of places to the right
Now divide as normal

Why it works: This is equivalent to multiplying both numbers by the same power of 10, which doesn't change the quotient.

Example: 7.2 ÷ 0.3

Step 1: Move the decimal in 0.3 one place right → 3

Step 2: Move the decimal in 7.2 one place right → 72

Step 3: Divide: 72 ÷ 3 = 24

Answer: 24

Verification: 24 × 0.3 = 7.2 ✓

Example: 4.86 ÷ 0.02

Step 1: Move decimals two places right: 486 ÷ 2

Step 2: Divide

Answer: 243

Visual Guide for Moving Decimals

Original: 7.2 ÷ 0.3

Move both decimals 1 place right:
7.2  →  72
0.3  →  3

Original: 4.86 ÷ 0.02

Move both decimals 2 places right:
4.86  →  486
0.02  →  2

Dividing by 10, 100, 1000

These are shortcuts — move the decimal point left:

Divide by 10: Move 1 place left

45.3 ÷ 10 = 4.53

Divide by 100: Move 2 places left

45.3 ÷ 100 = 0.453

Divide by 1000: Move 3 places left

45.3 ÷ 1000 = 0.0453

Why it works: Dividing by 10 is the inverse of multiplying by 10. Each division by 10 decreases the place value of each digit by one position.

Pattern:

Multiply by 10 → decimal moves right
Divide by 10 → decimal moves left

When Division Doesn't Come Out Even

Sometimes you'll get a remainder. Add zeros after the decimal point in the dividend and keep dividing.

Example: 5 ÷ 4

Steps:

4 into 5 = 1 remainder 1
Add decimal point and zero: 1.0 → bring down to get 10
4 into 10 = 2 remainder 2
Add another zero, bring down to get 20
4 into 20 = 5

Answer: 1.25

Example: 7 ÷ 8

Answer: 0.875

Repeating Decimals

Some divisions never end — they repeat forever!

Example: 1 ÷ 3 = 0.333333...

We write this as 0.3̄ (the bar means the 3 repeats)

Example: 2 ÷ 11 = 0.181818...

Written as 0.1̄8̄ (both digits repeat)

In practice: Round to a certain number of decimal places.

1 ÷ 3 ≈ 0.33 (rounded to 2 decimal places)

Estimating to Check Answers

Always estimate first.

Example: 7.2 ÷ 0.3

Estimate: Think 7 ÷ 0.3

Since 0.3 × 20 = 6 and 0.3 × 24 = 7.2
Answer should be around 20-24

Actual: 24 ✓ Makes sense!

Example: 4.86 ÷ 0.02

Estimate: 5 ÷ 0.02

0.02 × 100 = 2, so 0.02 × 250 = 5
Answer should be around 250

Actual: 243 ✓ Close!

Real-Life Applications

Sharing: "Divide $8.40 equally among 4 people"

$8.40 ÷ 4 = $2.10 per person

Unit price: "1.5 pounds costs $6.75. Price per pound?"

$6.75 ÷ 1.5
= $67.5 ÷ 15 (move decimals 1 place)
= $4.50 per pound

Conversion: "Run 10.5 km in 1.5 hours. Speed in km/hour?"

10.5 ÷ 1.5
= 105 ÷ 15 (move decimals 1 place)
= 7 km/hour

Common Mistakes

Mistake 1: Forgetting to move the decimal in the dividend

❌ 7.2 ÷ 0.3 → only changing divisor to 3 but keeping 7.2 ✓ Move both: 72 ÷ 3

Mistake 2: Not placing decimal point in quotient correctly

❌ Forgetting to put decimal point straight up ✓ Always align the decimal point vertically

Mistake 3: Moving decimals the wrong number of places

❌ 4.86 ÷ 0.02 → moving 1 place instead of 2 ✓ Count decimal places in divisor: 0.02 has 2 places, move 2

Tips for Success

Tip 1: When dividing by a decimal, move both decimals the same number of places

Tip 2: The decimal point in the answer goes straight up from the dividend

Tip 3: For dividing by 10, 100, 1000 — just move the decimal left (no long division needed!)

Tip 4: Always estimate to check if your answer makes sense

Tip 5: Add zeros after the decimal if division doesn't come out even

Practice

What is 9.6 ÷ 4?

What is 6.5 ÷ 0.5?

What is 240 ÷ 100?

What is 8.4 ÷ 0.2?