Understanding the concept
Decimals express fractions using powers of ten. The first digit after the decimal point is tenths, followed by hundredths and thousandths.
Start by identifying the quantities and units. Use a small example to understand the idea before attempting larger calculations.
Step-by-step method
Line up decimal points when adding or subtracting. For multiplication, estimate first and then check the decimal placement.
- Read the question and underline what you must find.
- Write down the given values and check their units.
- Apply the relevant method one step at a time.
- Estimate or reverse-check your answer before presenting it.
Quick-reference table
Use this reference to recognise common situations.
| Example | Meaning or method | Result |
|---|---|---|
| 0.1 | One tenth | 1/10 |
| 0.01 | One hundredth | 1/100 |
| 0.125 | 125 thousandths | 1/8 |
| 1.75 | One and seventy-five hundredths | 1¾ |
Four worked examples
Compare the different types of questions and the steps used to answer them.
Example 1: Shopping
Question or method: Add $3.45 and $2.80.
Example 2: Place value
Question or method: Write 0.307 as a sum.
Example 3: Compare numbers
Question or method: Compare 0.7 and 0.65.
Example 4: Measurement
Question or method: Convert 125 cm to metres.
Common mistakes
These errors are easy to make. Read each one and check your working.
- Assuming more decimal digits means a larger number.
- Misaligning decimal points in subtraction.
- Rounding too early in multi-step calculations.
Always ask whether your answer is reasonable for the original situation.
Practice questions
Try each question on paper before revealing the answer.
Question 1. Calculate 2.4 + 0.85.
Show answer and explanation
2.40 + 0.85 = 3.25.
Question 2. Calculate 5 − 1.75.
Show answer and explanation
5.00 − 1.75 = 3.25.
Question 3. Which is greater, 0.09 or 0.1?
Show answer and explanation
0.10 is greater than 0.09.
Question 4. Multiply 0.6 × 0.4.
Show answer and explanation
0.24.
Question 5. Round 3.146 to two decimal places.
Show answer and explanation
3.15 because the third decimal is 6.
Review checklist
- Can you explain the key idea in your own words?
- Can you complete a worked example without looking at the solution?
- Can you identify a common mistake and correct it?
- Can you estimate whether your result is sensible?