Worksheet titled "Significant Figures Worksheet" designed to help students practice identifying the number of significant figures in various numerical values, including decimals, scientific notation, and whole numbers.

Let's solve this Significant Figures Worksheet step by step. We'll go through each number and apply the rules for significant figures:

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🔢 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 there is a decimal point.
5. In scientific notation, only the digits in the coefficient matter.

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Now, let’s solve each one:

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✔ Solutions:

| Number | Significant Figures | Explanation |
|-------|---------------------|-----------|
| 1) 5050 | 3 | The zeros between 5 and 5 are significant, but trailing zero without decimal is not significant → 5, 0, 5 → 3 sig figs |
| 2) 0.0560 | 3 | Leading zeros not significant; 5, 6, and trailing zero after decimal are significant → 5, 6, 0 → 3 |
| 3) 0.000034 | 2 | Leading zeros not significant; only 3 and 4 are significant → 2 |
| 4) 0.0001500 | 4 | Leading zeros not significant; 1, 5, and two trailing zeros after decimal → 4 |
| 5) 37.300 | 5 | All digits are significant, including trailing zeros after decimal → 5 |
| 6) 1,060 | 3 | Trailing zero without decimal is not significant → 1, 0, 6 → 3 |
| 7) 5.050 × 10⁻² | 4 | Coefficient is 5.050 → all digits significant → 4 |
| 8) 180 | 2 | No decimal → trailing zero not significant → 1, 8 → 2 |
| 9) 4307 | 4 | All non-zero digits → 4 |
| 10) 0.70070 | 5 | Leading zero not significant; 7, 0, 0, 7, 0 → all zeros between or after non-zero with decimal → 5 |
| 11) 0.0 | 1 | Only the 0 after decimal is significant? Wait — actually, 0.0 has 1 significant figure because it's just one zero after decimal, indicating precision to tenths. But note: 0.0 means "zero" with precision to tenths → 1 sig fig |
| 12) 70900 | 3 | Trailing zeros without decimal → not significant → 7, 0, 9 → 3 |
| 13) 4206.0 | 5 | Decimal present → trailing zero is significant → 5 |
| 14) 100 | 1 | No decimal → only the 1 is significant → 1 |
| 15) 1.0200 × 10⁵ | 5 | Coefficient: 1.0200 → all digits significant → 5 |
| 16) 1508.06 | 6 | All digits significant, decimal present → 6 |
| 17) 0.0701 | 3 | Leading zeros not significant → 7, 0, 1 → 3 |
| 18) 0.04 | 1 | Leading zeros not significant → only the 4 → 1 |
| 19) 0.8008 | 4 | Leading zero not significant → 8, 0, 0, 8 → all significant → 4 |
| 20) 6060.0 | 5 | Decimal present → trailing zero is significant → 6, 0, 6, 0, 0 → 5 |

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✔ Final Answers:

| Number | Significant Figures |
|--------|---------------------|
| 1) 5050 | 3 |
| 2) 0.0560 | 3 |
| 3) 0.000034 | 2 |
| 4) 0.0001500 | 4 |
| 5) 37.300 | 5 |
| 6) 1,060 | 3 |
| 7) 5.050 × 10⁻² | 4 |
| 8) 180 | 2 |
| 9) 4307 | 4 |
| 10) 0.70070 | 5 |
| 11) 0.0 | 1 |
| 12) 70900 | 3 |
| 13) 4206.0 | 5 |
| 14) 100 | 1 |
| 15) 1.0200 × 10⁵ | 5 |
| 16) 1508.06 | 6 |
| 17) 0.0701 | 3 |
| 18) 0.04 | 1 |
| 19) 0.8008 | 4 |
| 20) 6060.0 | 5 |

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✔ Summary of Key Points:
- Trailing zeros are only significant if there's a decimal point.
- Leading zeros are never significant.
- In scientific notation, focus on the coefficient.
- Numbers like 0.0 or 100 without decimals have only one significant figure unless otherwise specified.

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