Significant figures and estimation worksheet | KS3-4 maths | Teachit - Free Printable

Let’s go step by step through each exercise. We’ll round numbers to the correct number of significant figures (sf) and do approximate calculations as instructed.

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Exercise A – Round to 1 significant figure

Rule: Look at the first non-zero digit. That’s your 1st sf. Look at the next digit — if it’s 5 or more, round up; if less than 5, leave it.

1. 320 → First digit is 3, next is 2 (<5) → 300
2. 475 → First digit 4, next is 7 (≥5) → 500
3. 5500 → First digit 5, next is 5 (≥5) → 6000
4. 2.8 → First digit 2, next is 8 (≥5) → 3
5. 76 → First digit 7, next is 6 (≥5) → 80
6. 32654 → First digit 3, next is 2 (<5) → 30000
7. 13.7 → First digit 1, next is 3 (<5) → 10
8. 0.09458 → First non-zero is 9, next is 4 (<5) → 0.09
9. 49.5 → First digit 4, next is 9 (≥5) → 50
10. 0.862 → First digit 8, next is 6 (≥5) → 0.9
11. 99 → First digit 9, next is 9 (≥5) → 100
12. 19500 → First digit 1, next is 9 (≥5) → 20000

✔ Exercise A Answers:
1. 300
2. 500
3. 6000
4. 3
5. 80
6. 30000
7. 10
8. 0.09
9. 50
10. 0.9
11. 100
12. 20000

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Exercise B – Round to 2 significant figures

Rule: Keep two digits starting from the first non-zero. Look at the third digit to decide rounding.

1. 825 → 8 and 2 are first two, next is 5 → round up → 830
2. 2.473 → 2 and 4, next is 7 → round up → 2.5
3. 8.95 → 8 and 9, next is 5 → round up → 9.0 (keep decimal to show 2 sf)
4. 5841 → 5 and 8, next is 4 → 5800
5. 261 → 2 and 6, next is 1 → 260
6. 0.05236 → first non-zero is 5, then 2, next is 3 → 0.052
7. 34821 → 3 and 4, next is 8 → round up → 35000
8. 5.953 → 5 and 9, next is 5 → round up → 6.0
9. 176.5 → 1 and 7, next is 6 → round up → 180

✔ Exercise B Answers:
1. 830
2. 2.5
3. 9.0
4. 5800
5. 260
6. 0.052
7. 35000
8. 6.0
9. 180

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Exercise C – Round to 3 significant figures

Rule: Keep three digits from first non-zero. Check fourth digit for rounding.

1. 7654 → 7,6,5 — next is 4 → 7650
2. 128.35 → 1,2,8 — next is 3 → 128
3. 25.862 → 2,5,8 — next is 6 → round up → 25.9
4. 44.98 → 4,4,9 — next is 8 → round up → 45.0
5. 125640 → 1,2,5 — next is 6 → round up → 126000
6. 0.054372 → first non-zero is 5, then 4,3 — next is 7 → round up → 0.0544

✔ Exercise C Answers:
1. 7650
2. 128
3. 25.9
4. 45.0
5. 126000
6. 0.0544

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Exercise D – Complete the table

We’ll round each number to 1 sf, 2 sf, and 3 sf.

| Number | Rounded to 1 sf | Rounded to 2 sf | Rounded to 3 sf |
|------------|------------------|------------------|------------------|
| 1. 2374 | 2000 | 2400 | 2370 |
| 2. 35253 | 40000 | 35000 | 35300 |
| 3. 5499 | 5000 | 5500 | 5500 |
| 4. 568.54 | 600 | 570 | 569 |
| 5. 7.3782 | 7 | 7.4 | 7.38 |
| 6. 953.75 | 1000 | 950 | 954 |
| 7. 64.95 | 60 | 65 | 65.0 |
| 8. 8054 | 8000 | 8100 | 8050 |
| 9. 99.8721 | 100 | 100 | 99.9 |
| 10. 0.3496 | 0.3 | 0.35 | 0.350 |
| 11. 0.2007 | 0.2 | 0.20 | 0.201 |
| 12. 0.006598| 0.007 | 0.0066 | 0.00660 |

Note: For decimals like 0.2007, leading zeros don’t count. First sf is 2, second is 0, third is 0 → so 0.201 when rounded to 3 sf.

✔ Exercise D Table filled above.

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Exercise E – Give an approximate answer

Instruction: Round EACH number to 1 significant figure BEFORE calculating.

1. 47 × 32 → 50 × 30 = 1500
2. 280 × 15.8 → 300 × 20 = 6000
3. 7.8 ÷ 0.352 → 8 ÷ 0.4 = 20
4. (5.36 + 2.83) / 0.475 → (5 + 3) / 0.5 = 8 / 0.5 = 16
5. 632 × 2.94 → 600 × 3 = 1800
6. 18.6 / 0.39 → 20 / 0.4 = 50
7. 0.675 × 0.425 → 0.7 × 0.4 = 0.28
8. (24.7 - 6.35) / 0.245 → (20 - 6) / 0.2 = 14 / 0.2 = 70
9. 64 ÷ 0.23 → 60 ÷ 0.2 = 300
10. (47.9 + 32.6) / (1.75 × 4.39) → (50 + 30) / (2 × 4) = 80 / 8 = 10
11. 0.61 ÷ 0.0175 → 0.6 ÷ 0.02 = 30
12. (43.5 × 5.63) / (34.8 - 9.67) → (40 × 6) / (30 - 10) = 240 / 20 = 12
13. 368 × 0.68 → 400 × 0.7 = 280
14. (12.7 × 4.35) / 0.18 → (10 × 4) / 0.2 = 40 / 0.2 = 200
15. 0.054 × 0.267 → 0.05 × 0.3 = 0.015
16. (84 × 6.33) / 32.5 → (80 × 6) / 30 = 480 / 30 = 16

✔ Exercise E Answers:
1. 1500
2. 6000
3. 20
4. 16
5. 1800
6. 50
7. 0.28
8. 70
9. 300
10. 10
11. 30
12. 12
13. 280
14. 200
15. 0.015
16. 16

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Final Answer:

Exercise A:
1. 300
2. 500
3. 6000
4. 3
5. 80
6. 30000
7. 10
8. 0.09
9. 50
10. 0.9
11. 100
12. 20000

Exercise B:
1. 830
2. 2.5
3. 9.0
4. 5800
5. 260
6. 0.052
7. 35000
8. 6.0
9. 180

Exercise C:
1. 7650
2. 128
3. 25.9
4. 45.0
5. 126000
6. 0.0544

Exercise D:
See completed table above.

Exercise E:
1. 1500
2. 6000
3. 20
4. 16
5. 1800
6. 50
7. 0.28
8. 70
9. 300
10. 10
11. 30
12. 12
13. 280
14. 200
15. 0.015
16. 16