Question

chapter 3 review questions
3.1 using and expressing measurements

1. three students made multiple weighings of a copper cylinder, each using a different balance. describe the accuracy and precision of each student’s measurements if the correct mass of the cylinder is 47.32 g.

mass of cylinder (g)
\tcolin\tlamont\tkevin
weighing 1\t47.13\t47.45\t47.95
weighing 2\t47.94\t47.39\t47.91
weighing 3\t46.83\t47.42\t47.89
weighing 4\t47.47\t47.41\t47.93

colin -
lamont -
kevin -

1. what are the 6 rules for significant figures? briefly summarize each.

a.
b.
c.
d.
e.
f.

Explanation:

Question 1: Analyzing Accuracy and Precision for Each Student

Colin:

• Precision: Colin's measurements (47.13, 47.94, 46.83, 47.47) are spread out (range = 47.94 - 46.83 = 1.11 g), so low precision.
• Accuracy: The average of Colin’s measurements is $\frac{47.13 + 47.94 + 46.83 + 47.47}{4} = \frac{189.37}{4} = 47.34$ g, close to 47.32 g, so moderate accuracy.

Lamont:

• Precision: Lamont’s measurements (47.45, 47.39, 47.42, 47.41) are close (range = 47.45 - 47.39 = 0.06 g), so high precision.
• Accuracy: The average is $\frac{47.45 + 47.39 + 47.42 + 47.41}{4} = \frac{189.67}{4} = 47.42$ g, slightly off 47.32 g, so good accuracy (close to true value).

Kevin:

• Precision: Kevin’s measurements (47.95, 47.91, 47.89, 47.93) are very close (range = 47.95 - 47.89 = 0.06 g), so high precision.
• Accuracy: The average is $\frac{47.95 + 47.91 + 47.89 + 47.93}{4} = \frac{191.68}{4} = 47.92$ g, far from 47.32 g, so low accuracy.

Question 2: 6 Rules for Significant Figures

Rule	Summary
b. Zeros between non - zeros	Zeros between two non - zero digits are significant. E.g., 405 has 3 sig figs.
c. Leading zeros	Zeros before the first non - zero digit are not significant (they are placeholders). E.g., 0.045 has 2 sig figs.
d. Trailing zeros in decimals	Zeros at the end of a number after a decimal point are significant. E.g., 4.50 has 3 sig figs.
e. Trailing zeros in whole numbers	Trailing zeros in a whole number without a decimal are ambiguous (but in scientific notation, they become significant). E.g., 4500 (without decimal) may have 2 or 4 sig figs; 4.5×10³ has 2, 4.500×10³ has 4.
f. Exact counts/definitions	Numbers from exact counts (e.g., 3 apples) or definitions (e.g., 1 m = 100 cm) have infinite sig figs.

Final Answers (Question 1)

• Colin: Low precision, moderate accuracy.
• Lamont: High precision, good accuracy.
• Kevin: High precision, low accuracy.

(For Question 2, the table above summarizes the 6 rules.)

Answer:

Question 1: Analyzing Accuracy and Precision for Each Student

Colin:

• Precision: Colin's measurements (47.13, 47.94, 46.83, 47.47) are spread out (range = 47.94 - 46.83 = 1.11 g), so low precision.
• Accuracy: The average of Colin’s measurements is $\frac{47.13 + 47.94 + 46.83 + 47.47}{4} = \frac{189.37}{4} = 47.34$ g, close to 47.32 g, so moderate accuracy.

Lamont:

• Precision: Lamont’s measurements (47.45, 47.39, 47.42, 47.41) are close (range = 47.45 - 47.39 = 0.06 g), so high precision.
• Accuracy: The average is $\frac{47.45 + 47.39 + 47.42 + 47.41}{4} = \frac{189.67}{4} = 47.42$ g, slightly off 47.32 g, so good accuracy (close to true value).

Kevin:

• Precision: Kevin’s measurements (47.95, 47.91, 47.89, 47.93) are very close (range = 47.95 - 47.89 = 0.06 g), so high precision.
• Accuracy: The average is $\frac{47.95 + 47.91 + 47.89 + 47.93}{4} = \frac{191.68}{4} = 47.92$ g, far from 47.32 g, so low accuracy.

Question 2: 6 Rules for Significant Figures

Rule	Summary
b. Zeros between non - zeros	Zeros between two non - zero digits are significant. E.g., 405 has 3 sig figs.
c. Leading zeros	Zeros before the first non - zero digit are not significant (they are placeholders). E.g., 0.045 has 2 sig figs.
d. Trailing zeros in decimals	Zeros at the end of a number after a decimal point are significant. E.g., 4.50 has 3 sig figs.
e. Trailing zeros in whole numbers	Trailing zeros in a whole number without a decimal are ambiguous (but in scientific notation, they become significant). E.g., 4500 (without decimal) may have 2 or 4 sig figs; 4.5×10³ has 2, 4.500×10³ has 4.
f. Exact counts/definitions	Numbers from exact counts (e.g., 3 apples) or definitions (e.g., 1 m = 100 cm) have infinite sig figs.

Final Answers (Question 1)

• Colin: Low precision, moderate accuracy.
• Lamont: High precision, good accuracy.
• Kevin: High precision, low accuracy.

(For Question 2, the table above summarizes the 6 rules.)