When to use a calculator
A calculator is a great tool when the numbers are messy or the calculation is long. But the thinking is still yours: deciding what to calculate, entering it correctly and checking the answer makes sense.
| Use mental maths | Use paper | Use a calculator |
|---|---|---|
| 50 × 4 | 346 + 278 | 37.86 × 4.29 |
| 1,000 − 1 | 1,248 ÷ 12 | √137 |
| 25% of 80 | 3/4 + 1/6 | Compound interest |
Good mathematicians choose the most efficient tool.
Basic vs scientific calculators
| Feature | Basic | Scientific calculator |
|---|---|---|
| +, −, ×, ÷ | ✓ | ✓ |
| Follows order of operations | often no | ✓ |
| Brackets | ✗ | ✓ |
| Powers (x², xʸ), roots | some | ✓ |
| Fractions, sin/cos/tan | ✗ | ✓ |
Test your calculator: enter 2 + 3 × 4. If it shows 14, it follows the order of operations. If it shows 20, it calculates left to right, and you’ll need to plan your entries.
Key buttons
| Button | Does |
|---|---|
| C / AC | Clears everything |
| CE / DEL | Clears or deletes the last entry |
| ( ) | Brackets |
| x² | Squares a number |
| ^ or xʸ | Raises to a power |
| √ | Square root |
| (−) | Makes a number negative (different from subtraction!) |
| M+, MR, MC | Memory: add to, recall, clear |
| Ans | Uses the previous answer |
Always estimate first
Calculator errors happen when we press wrong keys. Estimate before calculating.
Example: 48.7 × 21.3
- Estimate: 50 × 20 = 1,000.
- Calculator: 1,037.31 ✓ (close).
- If it showed 103.731 or 10,373.1, you’d know a key was missed.
Interpreting the display
- Long decimals: 10 ÷ 3 = 3.333333333. Use rounding to a sensible number of places (3.33).
- Money: 4.5 means $4.50.
- Scientific notation: 2.5E8 or 2.5 × 10⁸ means 250,000,000.
- Remainders: 47 ÷ 5 = 9.4, not "9 R4". The remainder is 0.4 × 5 = 2.
Computational strategies
- Break a long problem into steps and record each result.
- Use brackets or memory for multi-step expressions.
- Use Ans to chain calculations.
- Re-enter in a different order to double-check.
Worked examples
Example 1: Calculate (12.5 + 7.3) × 4.2 on a basic calculator without brackets.
Enter 12.5 + 7.3 = (19.8), then × 4.2 = → 83.16.
Example 2: Calculate √(5² + 12²).
5² + 12² = 169; √169 = 13.
Example 3: A calculator shows 1.2E5. What number is that?
1.2 × 10⁵ = 120,000.
Common mistakes
- Pressing subtract instead of the negative key, giving a syntax error.
- Forgetting brackets around numerators or denominators: (8 + 4) ÷ (5 − 2), not 8 + 4 ÷ 5 − 2.
- Copying too many decimal places, or rounding too early in a multi-step problem.
- Trusting the screen without estimating.
Try it yourself
- Estimate, then calculate: 19.6 × 5.1
- Calculate (34 + 18) ÷ (7 − 3).
- Round 22 ÷ 7 to two decimal places.
- What does 3.4E−3 mean?
Answers: 1) estimate 100; exact 99.96 2) 13 3) 3.14 4) 0.0034
Quick recap
- Choose mental, paper or calculator methods wisely.
- Estimate first and check the display makes sense.
- Use brackets, memory and sensible rounding.