Significant Figures Worksheets - Math Monks - Free Printable

To determine the number of significant figures in each number, we need to follow the rules for significant figures:

Rules for Significant Figures:

1. Non-zero digits are always significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (zeros before the first non-zero digit) are not significant.
4. Trailing zeros (zeros after the last non-zero digit) are significant if they are to the right of a decimal point or if a decimal point is explicitly placed after them.
5. In scientific notation, only the digits in the coefficient are considered significant.

Let's solve each number step by step:

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Column 1:

1. 5050
- Non-zero digits: 5, 0, 5, 0
- Trailing zeros are not significant because there is no decimal point.
- Significant Figures: 3

2. 0.0560
- Leading zeros: 0, 0 (not significant)
- Non-zero digits: 5, 6, 0 (trailing zero is significant because it is after the decimal point)
- Significant Figures: 3

3. 0.000034
- Leading zeros: 0, 0, 0, 0 (not significant)
- Non-zero digits: 3, 4
- Significant Figures: 2

4. 0.0001500
- Leading zeros: 0, 0, 0, 0 (not significant)
- Non-zero digits: 1, 5, 0, 0 (trailing zeros are significant because they are after the decimal point)
- Significant Figures: 4

5. 37.300
- Non-zero digits: 3, 7, 3, 0, 0 (trailing zeros are significant because they are after the decimal point)
- Significant Figures: 5

6. 1,060
- Non-zero digits: 1, 0, 6, 0
- Trailing zeros are not significant because there is no decimal point.
- Significant Figures: 3

7. 5.050 × 10²
- Coefficient: 5.050
- Non-zero digits: 5, 0, 5, 0 (trailing zero is significant because it is after the decimal point)
- Significant Figures: 4

8. 180
- Non-zero digits: 1, 8, 0
- Trailing zero is not significant because there is no decimal point.
- Significant Figures: 2

9. 4307
- Non-zero digits: 4, 3, 0, 7
- Zero is between non-zero digits and is significant.
- Significant Figures: 4

10. 0.70070
- Leading zero: 0 (not significant)
- Non-zero digits: 7, 0, 0, 7, 0 (trailing zero is significant because it is after the decimal point)
- Significant Figures: 5

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Column 2:

11. 0.0
- Leading zeros: 0, 0 (not significant)
- No non-zero digits.
- Significant Figures: 0

12. 70900
- Non-zero digits: 7, 0, 9, 0, 0
- Trailing zeros are not significant because there is no decimal point.
- Significant Figures: 3

13. 4206.0
- Non-zero digits: 4, 2, 0, 6, 0 (trailing zero is significant because it is after the decimal point)
- Significant Figures: 5

14. 100
- Non-zero digits: 1, 0, 0
- Trailing zeros are not significant because there is no decimal point.
- Significant Figures: 1

15. 1.0200 × 10⁵
- Coefficient: 1.0200
- Non-zero digits: 1, 0, 2, 0, 0 (trailing zeros are significant because they are after the decimal point)
- Significant Figures: 5

16. 1508.06
- Non-zero digits: 1, 5, 0, 8, 0, 6
- All digits are significant.
- Significant Figures: 6

17. 0.0701
- Leading zeros: 0, 0 (not significant)
- Non-zero digits: 7, 0, 1
- Significant Figures: 3

18. 0.04
- Leading zeros: 0, 0 (not significant)
- Non-zero digits: 4
- Significant Figures: 1

19. 0.8008
- Leading zero: 0 (not significant)
- Non-zero digits: 8, 0, 0, 8
- Zeros between non-zero digits are significant.
- Significant Figures: 4

20. 6060.0
- Non-zero digits: 6, 0, 6, 0, 0 (trailing zero is significant because it is after the decimal point)
- Significant Figures: 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 × 10² | 4 |
| 8) 180 | 2 |
| 9) 4307 | 4 |
| 10) 0.70070 | 5 |
| 11) 0.0 | 0 |
| 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 |

Boxed Answer:
\[
\boxed{
\begin{array}{c|c}
\text{Number} & \text{Significant Figures} \\
\hline
1) 5050 & 3 \\
2) 0.0560 & 3 \\
3) 0.000034 & 2 \\
4) 0.0001500 & 4 \\
5) 37.300 & 5 \\
6) 1,060 & 3 \\
7) 5.050 \times 10^2 & 4 \\
8) 180 & 2 \\
9) 4307 & 4 \\
10) 0.70070 & 5 \\
11) 0.0 & 0 \\
12) 70900 & 3 \\
13) 4206.0 & 5 \\
14) 100 & 1 \\
15) 1.0200 \times 10^5 & 5 \\
16) 1508.06 & 6 \\
17) 0.0701 & 3 \\
18) 0.04 & 1 \\
19) 0.8008 & 4 \\
20) 6060.0 & 5 \\
\end{array}
}
\]