Significant Figures Worksheet - Free Printable

Let's solve each of these problems step by step using the rules for significant figures:

---

🔢 Rules for Significant Figures:

1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (before the first non-zero digit) are NOT significant.
4. Trailing zeros (after the last non-zero digit) are significant ONLY if the number has a decimal point.
5. In scientific notation, only the digits in the coefficient are considered; the power of 10 does not affect significance.

---

Now, let’s go through each number:

---

✔ Solutions:

| Number | Significant Figures | Explanation |
|-------|---------------------|-----------|
| 1. 357 | 3 | All non-zero digits → 3, 5, 7 |
| 2. 10000 | 1 | No decimal → trailing zeros are not significant |
| 3. 51015 | 5 | All digits are non-zero or between non-zeros → 5,1,0,1,5 |
| 4. 6.060 × 10⁻² | 4 | Coefficient: 6.060 → all digits significant (zeros between and after non-zero digits) |
| 5. 0.0007 | 1 | Leading zeros not significant; only the 7 is significant |
| 6. 4.556 × 10⁹ | 4 | Coefficient: 4.556 → all digits are significant |
| 7. 5050 | 3 | Trailing zero without decimal → not significant. So 5, 0, 5 → 3 sig figs |
| 8. 5050.0 | 5 | Decimal present → trailing zero is significant → 5,0,5,0,0 |
| 9. 6.8 × 10³ | 2 | Coefficient: 6.8 → two significant digits |
| 10. 0.002110 | 4 | Leading zeros not significant. 2,1,1,0 → the trailing zero after decimal is significant |
| 11. 33.303 | 5 | All digits are significant (including zero between non-zeros) |
| 12. 170 | 2 | No decimal → trailing zero not significant → 1 and 7 |
| 13. 15.0 × 10⁻⁵ | 3 | Coefficient: 15.0 → the zero after decimal is significant → 1,5,0 |
| 14. 0.7007 | 4 | Leading zero not significant; 7,0,0,7 → both zeros between non-zeros are significant |
| 15. 0.70070 | 5 | Same as above, but with an extra trailing zero after decimal → 7,0,0,7,0 → all significant |
| 16. 4206 | 4 | All non-zero digits → 4,2,0,6 → zero between non-zeros is significant |
| 17. 0.02 | 1 | Only the 2 is significant; leading zeros not significant |
| 18. 10.01 | 4 | Zeros between non-zeros are significant → 1,0,0,1 |
| 19. 0 | 1 | Zero alone is considered to have one significant figure (by convention) |
| 20. 0.0 | 1 | This is ambiguous, but typically interpreted as having 1 significant figure, since it's just a placeholder showing precision at zero |

> ⚠️ Note: For #19 and #20, some sources say "0" has no significant figures, but in most educational contexts, especially when measuring, 0 is considered to have one significant figure if it represents a measured value.

---

✔ Final Answers:

| Number | Significant Figures |
|--------|---------------------|
| 1. 357 | 3 |
| 2. 10000 | 1 |
| 3. 51015 | 5 |
| 4. 6.060 × 10⁻² | 4 |
| 5. 0.0007 | 1 |
| 6. 4.556 × 10⁹ | 4 |
| 7. 5050 | 3 |
| 8. 5050.0 | 5 |
| 9. 6.8 × 10³ | 2 |
| 10. 0.002110 | 4 |
| 11. 33.303 | 5 |
| 12. 170 | 2 |
| 13. 15.0 × 10⁻⁵ | 3 |
| 14. 0.7007 | 4 |
| 15. 0.70070 | 5 |
| 16. 4206 | 4 |
| 17. 0.02 | 1 |
| 18. 10.01 | 4 |
| 19. 0 | 1 |
| 20. 0.0 | 1 |

---

✔ Summary:
You can now fill in the blanks on the worksheet accordingly.

Let me know if you want this as a printable PDF or need help understanding any specific rule!