Accuracy And Precision Worksheet 2020-2024 - Fill and Sign ... - Free Printable

Problem Analysis:

The task involves understanding and applying the concept of significant figures in measurements. Significant figures are crucial for conveying the precision of a measurement. The problem provides examples and asks you to determine the number of significant figures in given measurements.

#### Key Points About Significant Figures:
1. Definition: Significant figures represent the digits in a measured value that carry meaningful information about its precision.
2. Rules for Determining Significant Figures:
- Non-zero digits are always significant.
- Zeros between non-zero digits are significant.
- Leading zeros (before the first non-zero digit) are not significant.
- Trailing 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 shown.
- Exact numbers (like counts or defined constants) have an infinite number of significant figures.

#### Task Breakdown:
The problem provides several measurements and asks you to determine the number of significant figures in each. Let's solve it step by step.

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Solution:

#### Measurement 1: \( 3.87 \, \text{m} \)
- The number is \( 3.87 \).
- All non-zero digits are significant.
- There are 3 significant figures.

#### Measurement 2: \( 790.000 \, \text{kg} \)
- The number is \( 790.000 \).
- All non-zero digits are significant.
- The trailing zeros after the decimal point are also significant.
- There are 6 significant figures.

#### Measurement 3: \( 0.0031 \, \text{s} \)
- The number is \( 0.0031 \).
- Leading zeros are not significant.
- The digits \( 3 \) and \( 1 \) are significant.
- There are 2 significant figures.

#### Measurement 4: \( 20.000 \, \text{g} \)
- The number is \( 20.000 \).
- All non-zero digits are significant.
- The trailing zeros after the decimal point are significant.
- There are 5 significant figures.

#### Measurement 5: \( 17.00 \, \text{cm} \)
- The number is \( 17.00 \).
- All non-zero digits are significant.
- The trailing zeros after the decimal point are significant.
- There are 4 significant figures.

#### Measurement 6: \( 0.004 \, \text{m}^3 \)
- The number is \( 0.004 \).
- Leading zeros are not significant.
- The digit \( 4 \) is significant.
- There is 1 significant figure.

#### Measurement 7: \( 29.0 \, \text{cm} \)
- The number is \( 29.0 \).
- All non-zero digits are significant.
- The trailing zero after the decimal point is significant.
- There are 3 significant figures.

#### Measurement 8: \( 98.0 \, \text{°C} \)
- The number is \( 98.0 \).
- All non-zero digits are significant.
- The trailing zero after the decimal point is significant.
- There are 3 significant figures.

#### Measurement 9: \( 39.4^\circ \, \text{F} \)
- The number is \( 39.4 \).
- All non-zero digits are significant.
- There are 3 significant figures.

#### Measurement 10: \( 15.9 \, \text{mm} \)
- The number is \( 15.9 \).
- All non-zero digits are significant.
- There are 3 significant figures.

#### Measurement 11: \( 0.7 \, \text{cm} \)
- The number is \( 0.7 \).
- Leading zeros are not significant.
- The digit \( 7 \) is significant.
- There is 1 significant figure.

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Final Answer:

\[
\boxed{
\begin{array}{ll}
3.87 \, \text{m} & 3 \\
790.000 \, \text{kg} & 6 \\
0.0031 \, \text{s} & 2 \\
20.000 \, \text{g} & 5 \\
17.00 \, \text{cm} & 4 \\
0.004 \, \text{m}^3 & 1 \\
29.0 \, \text{cm} & 3 \\
98.0 \, \text{°C} & 3 \\
39.4^\circ \, \text{F} & 3 \\
15.9 \, \text{mm} & 3 \\
0.7 \, \text{cm} & 1 \\
\end{array}
}
\]