Decimal Operations
Master adding, subtracting, multiplying and dividing with decimals. These skills are essential for working with money, measurements and real-world problems.
Adding and Subtracting Decimals
The most important rule: line up the decimal points. This ensures ones are under ones, tenths under tenths, and so on. Add trailing zeros if needed so both numbers have the same number of decimal places.
Adding: 14.6 + 3.25
1 4 . 6 0
+ 3 . 2 5
1 7 . 8 5
Add a zero to 14.6 to make 14.60
Subtracting: 20.5 - 8.73
2 0 . 5 0
- 8 . 7 3
1 1 . 7 7
Add a zero to 20.5 to make 20.50
Multiplying Decimals
To multiply decimals: ignore the decimal points, multiply as whole numbers, then count the total decimal places in both numbers and put the decimal point in the answer.
Example: 3.4 × 2.5
Step 1: Ignore decimals: 34 × 25 = 850
Step 2: Count decimal places: 3.4 has 1, 2.5 has 1. Total = 2 decimal places.
Step 3: Place the decimal: 850 → 8.50 = 8.5
Money Example
You buy 6 oranges at $1.35 each. Total = 6 × $1.35 = $8.10
Dividing Decimals
To divide a decimal by a whole number, set up the long division as normal and keep the decimal point in the same position in your answer.
Example: 15.6 ÷ 4
Step 1: 4 into 15 goes 3 times (12). Remainder 3.
Step 2: Place the decimal point. Bring down 6 to get 36.
Step 3: 4 into 36 goes 9 times exactly.
Answer: 3.9
Dividing by a Decimal
To divide by a decimal (e.g. 6.4 ÷ 0.2), multiply both numbers by 10 to make the divisor a whole number: 64 ÷ 2 = 32.
Decimals and Money
Australian dollars and cents use decimals every day. The dollar amount is before the decimal point and cents come after (always 2 decimal places).
Example: Shopping Problem
You buy a sandwich for $7.50, a juice for $3.95 and a piece of fruit for $1.20. How much change do you get from $20?
Step 1: Total = $7.50 + $3.95 + $1.20 = $12.65
Step 2: Change = $20.00 - $12.65 = $7.35
Key Vocabulary
Decimal Point
The dot that separates whole numbers from fractional parts (e.g. in 3.75, the decimal point is between 3 and 75).
Tenths
The first digit after the decimal point. Each tenth is one part out of 10 (e.g. 0.3 = three tenths).
Hundredths
The second digit after the decimal point. Each hundredth is one part out of 100 (e.g. 0.07 = seven hundredths).
Trailing Zero
A zero added at the end of a decimal that does not change its value (e.g. 4.5 = 4.50).
Worked Examples
Calculate 45.8 + 7.36
Step 1: Line up decimal points. Write 45.80 (add trailing zero).
Step 2: Add: 0 + 6 = 6, 8 + 3 = 11 (write 1 carry 1), 5 + 7 + 1 = 13 (write 3 carry 1), 4 + 1 = 5.
Answer: 53.16
Calculate 0.6 × 0.4
Step 1: Ignore decimals: 6 × 4 = 24
Step 2: Count decimal places: 1 + 1 = 2 decimal places.
Answer: 0.24
Three friends share a bill of $47.10 equally. How much does each pay?
Step 1: Divide: $47.10 ÷ 3
Step 2: 3 into 47 goes 15 times (45), remainder 2. Bring down 1 to make 21. 3 into 21 = 7. Bring down 0. 3 into 0 = 0.
Answer: Each person pays $15.70
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is 6.45 + 3.8?
Question 2
What is 12.00 - 4.63?
Question 3
What is 2.5 × 1.2?
Question 4
What is 18.6 ÷ 3?
Question 5
You buy 4 notebooks at $2.75 each. What is the total cost?
Key Concepts Summary
- ●When adding or subtracting decimals, always line up the decimal points.
- ●Add trailing zeros so both numbers have the same number of decimal places.
- ●When multiplying decimals, multiply as whole numbers then count total decimal places.
- ●When dividing, keep the decimal point in the same position in the answer.
- ●Use estimation to check your answers are sensible.