This worksheet helps students practice identifying significant figures in various measurements and performing addition with correct precision.

Let's solve this Significant Figures Worksheet step by step.

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🔹 Part 1: Determine the number of significant figures in each number

We use the rules for significant figures:

1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (before non-zero digits) are NOT significant.
4. Trailing zeros (after non-zero digits) are significant only if there is a decimal point.
5. In scientific notation, only the digits in the coefficient are considered.

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#### ✔ Answers to Part 1:

| Number | Significant Figures | Explanation |
|--------|---------------------|-----------|
| 1. 5.432 g | 4 | All non-zero digits → 4 sig figs |
| 2. 40.319 g | 5 | Zero between non-zeros → significant |
| 3. 145 cm³ | 3 | All non-zero → 3 sig figs |
| 4. 0.189 lb | 3 | Leading zero not significant; 1,8,9 → 3 |
| 5. 429.3 g | 4 | All digits non-zero, decimal present → 4 |
| 6. 429.30 g | 5 | Trailing zero after decimal → significant |
| 7. 2873.0 cm³ | 5 | Trailing zero after decimal → significant |
| 8. 99.9 mL | 3 | All non-zero digits → 3 |
| 9. 0.000235 g | 3 | Leading zeros not significant; 2,3,5 → 3 |
| 10. 144 lb | 3 | All non-zero → 3 |
| 11. 2500 cm | 2 | No decimal → trailing zeros not significant |
| 12. 2500.0 cm | 5 | Decimal present → all zeros significant |
| 13. 1.04 × 10¹⁴ | 3 | Coefficient: 1,0,4 → 3 sig figs |
| 14. 3.58 × 10¹⁴ | 3 | Coefficient: 3,5,8 → 3 |
| 15. 48.57193 oz | 7 | All digits significant → 7 |
| 16. 8365.6 g | 5 | All digits significant → 5 |
| 17. 0.002300 mg | 4 | Leading zeros not significant; 2,3,0,0 → 4 (trailing zeros after decimal) |
| 18. 7.500 × 10⁸ | 4 | Coefficient: 7,5,0,0 → 4 sig figs |
| 19. 3.92 × 10⁻⁴ | 3 | Coefficient: 3,9,2 → 3 |
| 20. 1.000 × 10³ | 4 | Coefficient: 1,0,0,0 → 4 sig figs |

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🔹 Part 2: Add measurements and round to correct significant figures

When adding or subtracting, the result should be rounded to the least precise decimal place (i.e., the number with the fewest decimal places).

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#### ✔ Problem 21:
12 cm + 0.031 cm + 7.959 cm = ?

- Step 1: Add
$$
12 + 0.031 + 7.959 = 19.990 \text{ cm}
$$

- Step 2: Look at decimal places:
- 12 → no decimal (precision to ones place)
- 0.031 → 3 decimal places
- 7.959 → 3 decimal places
→ The least precise is 12 cm (to the nearest cm)

- So, round 19.990 to the nearest whole number → 20 cm

✔ Answer: 20 cm

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#### ✔ Problem 22:
0.085 cm + 0.062 cm = ?

- Add:
$$
0.085 + 0.062 = 0.147 \text{ cm}
$$

- Both have 3 decimal places, so answer has 3 decimal places.

✔ Answer: 0.147 cm

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#### ✔ Problem 23:
3.410 g + 3.912 g + 7.0518 g + 0.00013 g = ?

- Add:
$$
3.410 + 3.912 = 7.322 \\
7.322 + 7.0518 = 14.3738 \\
14.3738 + 0.00013 = 14.37393 \text{ g}
$$

- Now check decimal places:
- 3.410 → 3 decimals
- 3.912 → 3 decimals
- 7.0518 → 4 decimals
- 0.00013 → 5 decimals

→ Least precise is 3 decimal places

→ Round 14.37393 to 3 decimal places → 14.374 g

✔ Answer: 14.374 g

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#### ✔ Problem 24:
30.5 g + 16.82 g + 410.07 g + 85.219 g = ?

- Add:
$$
30.5 + 16.82 = 47.32 \\
47.32 + 410.07 = 457.39 \\
457.39 + 85.219 = 542.609 \text{ g}
$$

- Check decimal places:
- 30.5 → 1 decimal
- 16.82 → 2 decimals
- 410.07 → 2 decimals
- 85.219 → 3 decimals

→ Least precise: 30.5 g → 1 decimal place

→ Round 542.609 to 1 decimal place → 542.6 g

✔ Answer: 542.6 g

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#### ✔ Problem 25:
143.0 cm + 289.25 cm + 68.45 cm + 6.00 cm = ?

- Add:
$$
143.0 + 289.25 = 432.25 \\
432.25 + 68.45 = 499.70 \\
499.70 + 6.00 = 505.70 \text{ cm}
$$

- Check decimal places:
- 143.0 → 1 decimal
- 289.25 → 2 decimals
- 68.45 → 2 decimals
- 6.00 → 2 decimals

→ Least precise: 143.0 cm → 1 decimal place

→ Round 505.70 to 1 decimal place → 505.7 cm

✔ Answer: 505.7 cm

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✔ Final Answers Summary:

#### Part 1: Significant Figures
1. 4
2. 5
3. 3
4. 3
5. 4
6. 5
7. 5
8. 3
9. 3
10. 3
11. 2
12. 5
13. 3
14. 3
15. 7
16. 5
17. 4
18. 4
19. 3
20. 4

#### Part 2: Addition with Sig Figs
21. 20 cm
22. 0.147 cm
23. 14.374 g
24. 542.6 g
25. 505.7 cm

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