Rounding & Estimation — Grade 3 Mathematics
Rounding replaces a number with a simpler, approximate value. In Grade 3, we round to the nearest 10, 100 and 1 000, then use rounded numbers to estimate the results of calculations without needing exact working.
The Rounding Rule
Look at the digit immediately to the RIGHT of the place you are rounding to:
• If it is 0, 1, 2, 3 or 4 → round DOWN (keep the digit the same, fill remaining places with 0).
• If it is 5, 6, 7, 8 or 9 → round UP (add 1 to the rounding digit, fill remaining places with 0).
• If it is 0, 1, 2, 3 or 4 → round DOWN (keep the digit the same, fill remaining places with 0).
• If it is 5, 6, 7, 8 or 9 → round UP (add 1 to the rounding digit, fill remaining places with 0).
| Number | Nearest 10 | Nearest 100 | Nearest 1 000 |
|---|---|---|---|
| 4 736 | 4 740 | 4 700 | 5 000 |
| 8 295 | 8 300 | 8 300 | 8 000 |
| 6 050 | 6 050 | 6 100 | 6 000 |
| 9 999 | 10 000 | 10 000 | 10 000 |
Using Rounding to Estimate
Round each number before calculating, then perform the simple calculation.
The result is an estimate (≈ means "approximately equal to").
Example: 387 + 512 ≈ 400 + 500 = 900 (actual: 899 — very close!)
The result is an estimate (≈ means "approximately equal to").
Example: 387 + 512 ≈ 400 + 500 = 900 (actual: 899 — very close!)
💡 Why estimate? Quick check to see if an exact answer is in the right ballpark — catches big errors before they matter!
Worked Examples
Example 1 — Rounding to Nearest 100
Round these numbers to the nearest 100: (a) 3 748 (b) 5 650 (c) 2 049
- (a) Look at T digit: 4 < 5 → round down → 3 700
- (b) Look at T digit: 5 ≥ 5 → round up → 5 700
- (c) Look at T digit: 4 < 5 → round down → 2 000
Example 2 — Estimating an Addition
Estimate: 3 812 + 2 467
- Round to nearest 1 000: 3 812 ≈ 4 000; 2 467 ≈ 2 000
- Estimate: 4 000 + 2 000 = 6 000
- Exact: 6 279 — estimate is reasonable ✓
Example 3 — Real World: Shopping Budget 🛒
Items cost £2.89, £4.15, and £3.72. Estimate the total to check if £10 is enough.
- Round to nearest £1: £3 + £4 + £4 = £11
- Estimate ≈ £11 — £10 is NOT enough.
- Exact: £2.89 + £4.15 + £3.72 = £10.76 (confirms estimate)
Practice Questions
1. Round 7 382 to the nearest 100.
✅ T digit = 8 ≥ 5 → round up → 7 400
2. Round 5 499 to the nearest 1 000.
✅ H digit = 4 < 5 → round down → 5 000
3. Estimate 4 623 − 2 198 by rounding to the nearest 1 000.
✅ 5 000 − 2 000 = ≈ 3 000 (exact: 2 425)
4. Which is a better estimate for 348 × 6: 300 × 6 or 350 × 6?
✅ 348 rounds to 350 (T digit 4 → no, 8≥5... wait: nearest 10: 350, nearest 100: 300). 350 × 6 = 2 100 is the better estimate (exact: 2 088).
5. A school has 1 248 boys and 1 356 girls. Estimate the total number of pupils to the nearest 100.
✅ 1 200 + 1 400 = ≈ 2 600 (exact: 2 604)
Key Points to Remember
- Check the digit one place to the right of where you are rounding.
- Digit 0–4 → round down (keep rounding digit same). Digit 5–9 → round up.
- Use ≈ to show an answer is an estimate, not exact.
- Rounding to a larger place value (e.g., nearest 1 000) gives a rougher estimate but is quicker.
- Use estimates to check whether exact answers are reasonable.