Dividing Decimals

Two kinds of decimal division

Dividing decimals splits into two cases, and each has a simple rule:

1. Dividing by a whole number — divide as usual and keep the point lined up.
2. Dividing by a decimal — first turn the divisor into a whole number, then use case 1.

Case 1: dividing a decimal by a whole number

Keep the decimal point in the answer directly above the point in the number you are dividing.

Worked example 1: 6.4 ÷ 2

• 6 ÷ 2 = 3
• 0.4 ÷ 2 = 0.2
• Answer: 3.2

Worked example 2: 9.6 ÷ 4 (using short division)

   2 . 4
 4 ) 9 . 6

• 9 ÷ 4 = 2 remainder 1. Carry the 1 to make 16.
• Bring down with the point, 16 ÷ 4 = 4.
• Answer: 2.4.

If a division does not stop neatly, add zeros after the decimal point and keep going. For example, 5 ÷ 4 becomes 5.00 ÷ 4 = 1.25.

Case 2: dividing by a decimal

You can only divide easily by whole numbers, so first make the divisor whole. The trick: multiply both numbers by the same power of 10. This keeps the answer unchanged, because it is the same as multiplying the fraction top and bottom by the same number.

Worked example 3: 4.8 ÷ 0.6

1. The divisor 0.6 has 1 decimal place → multiply both numbers by 10.
2. 4.8 × 10 = 48, and 0.6 × 10 = 6.
3. Now divide the whole numbers: 48 ÷ 6 = 8.

Worked example 4: 7.5 ÷ 0.25

1. The divisor 0.25 has 2 decimal places → multiply both by 100.
2. 7.5 × 100 = 750, and 0.25 × 100 = 25.
3. 750 ÷ 25 = 30.

Why moving both points keeps the answer the same

A division is just a fraction. 4.8 ÷ 0.6 is the fraction 4.8/0.6. Multiplying the top and bottom by 10 gives 48/6 — an equivalent fraction, so the value is identical:

4.8/0.6 = (4.8 × 10)/(0.6 × 10) = 48/6 = 8

This is the same equivalent-fraction idea behind simplifying. You move the point in both numbers by the same amount, never just one.

Why dividing can make numbers bigger

Division asks "how many fit?" When you divide by a number smaller than 1, lots of those small pieces fit, so the answer is bigger than what you started with.

Divide by	Effect	Example
more than 1 (e.g. 4)	answer gets smaller	8 ÷ 4 = 2
exactly 1	answer stays the same	8 ÷ 1 = 8
less than 1 (e.g. 0.5)	answer gets bigger	8 ÷ 0.5 = 16
much less than 1 (e.g. 0.1)	answer gets much bigger	8 ÷ 0.1 = 80

Dividing by 0.5 is the same as asking "how many halves?", which doubles the number. Dividing by 0.1 means "how many tenths?", which multiplies by 10.

Estimate to check

Before dividing, round both numbers and do an easy division.

Example: 11.8 ÷ 3.9 → round to 12 ÷ 4 = 3, so expect about 3. The exact answer is about 3.03, which matches. If you had got 0.3 or 30, the estimate would flag the slip.

Try it yourself: sharing fairly

• A 3.6 m ribbon is cut into 4 equal pieces. How long is each? (3.6 ÷ 4)
• A $7.50 pizza is split among 5 friends. What does each pay? (7.50 ÷ 5)
• How many 0.25 litre cups fill a 2 litre jug? (2 ÷ 0.25)

Estimate each first, then divide and check the answer is sensible.

Why this matters

Dividing decimals lets you share money, split measurements and find unit prices. It builds straight on multiplying decimals and the place-value foundation in decimals explained.