Rounding & Estimation — Grade 5 Mathematics
In Grade 5, we round decimals to any number of decimal places, round large numbers to significant figures, and use rounding to estimate the results of complex, multi-step calculations.
Rounding Decimals
Look at the digit one place to the right of where you are rounding.
5 or more → round up; 4 or less → round down (truncate).
5 or more → round up; 4 or less → round down (truncate).
| Number | 1 d.p. | 2 d.p. | 3 d.p. |
|---|---|---|---|
| 7.4836 | 7.5 | 7.48 | 7.484 |
| 12.0954 | 12.1 | 12.10 | 12.095 |
| 0.9997 | 1.0 | 1.00 | 1.000 |
Significant Figures
Significant figures (s.f.) count from the first non-zero digit.
• 4 827 to 1 s.f. = 5 000 (leading digit 4 → round up because next digit is 8)
• 0.007 36 to 2 s.f. = 0.0074 (first s.f. = 7, second s.f. = 3; next digit 6 → round up)
• 1 234.5 to 3 s.f. = 1 230
• 4 827 to 1 s.f. = 5 000 (leading digit 4 → round up because next digit is 8)
• 0.007 36 to 2 s.f. = 0.0074 (first s.f. = 7, second s.f. = 3; next digit 6 → round up)
• 1 234.5 to 3 s.f. = 1 230
💡 Key: Zeros before the first non-zero digit do NOT count as significant figures. 0.0074 has 2 significant figures.
Worked Examples
Example 1 — Round to 2 Decimal Places
Round 8.3762 to 2 decimal places.
- Look at the 3rd decimal place: 6 ≥ 5 → round up
- 2nd decimal place 7 → becomes 8
- Answer: 8.38
Example 2 — Significant Figures
Round 0.009 47 to 2 significant figures.
- First s.f. = 9 (in thousandths position)
- Second s.f. = 4; look at next digit: 7 ≥ 5 → round up 4 to 5
- Answer: 0.0095
Example 3 — Estimate a Complex Calculation 🔢
Estimate √(48.7 × 6.1) using rounding to 1 s.f.
- 48.7 ≈ 50; 6.1 ≈ 6
- 50 × 6 = 300
- √300 ≈ √289 = 17 → estimate ≈ 17
- Exact: √297.07 ≈ 17.24 — close ✓
Practice Questions
1. Round 6.3847 to 1 decimal place.
✅ 2nd decimal place is 3 < 5 → round down: 6.4
2. Round 4.7956 to 2 decimal places.
✅ 3rd d.p. = 5 → round up: 4.80
3. Round 36 482 to 2 significant figures.
✅ 1st s.f. = 3, 2nd s.f. = 6; next digit 4 < 5 → round down: 36 000
4. Estimate 29.4 × 51.6 using 2 significant figures.
✅ 29.4 ≈ 29; 51.6 ≈ 52; estimate = 30 × 50 = 1 500 (exact: 1 517.04)
5. Round 0.006 382 to 2 significant figures.
✅ First s.f. = 6; second s.f. = 3; next digit 8 ≥ 5 → round up: 0.0064
Key Points to Remember
- Rounding decimals: look at the digit one place to the right of your rounding position.
- 5 or more → round up; 4 or less → round down.
- Significant figures start counting from the first non-zero digit.
- Zeros before the first non-zero digit are not significant.
- Estimation: round all numbers first, then compute — use ≈ in your answer.