Significant Figures Practice

Instructions

This worksheet will help you practice with significant figures (sig figs). First, you will practice identifying them, then you will use them in calculations. Good luck!

Rules for Significant Figures: A Quick Guide

1. Non-zero digits (1-9) are always significant.

2. Captive zeros (zeros between other sig figs) are always significant (e.g., 101 has 3 sig figs).

3. Leading zeros (zeros at the beginning of a number) are never significant (e.g., 0.005 has 1 sig fig).

4. Trailing zeros (zeros at the end of a number) are only significant if there is a decimal point in the number (e.g., 100 has 1 sig fig, but 100. has 3 sig figs).

Part 1: How Many Sig Figs?

For each number below, write how many significant figures it contains.

1. 45.89 _________

2. 0.0051 _________

3. 505.0 _________

4. 1,000 _________

5. 1,000. _________

6. 8.50 x 10^3 _________

Part 2: Calculations with Significant Figures

Solve the following problems. Make sure to round your final answer to the correct number of significant figures!

Remember the Rules:

• Multiplication & Division: Round your answer to match the measurement with the fewest sig figs.

• Addition & Subtraction: Round your answer to match the measurement with the fewest decimal places

7. 2.50 g / 0.50 s = ___________________

8. 12.52 m * 1.3 m = ___________________

9. 100.55 L - 5.1 L = ___________________

10. 22.4 g + 1.25 g = ___________________

11. (15.2 cm * 3.5 cm) / 2.05 cm = ___________________

Challenge Problem

1. A student measures the sides of a rectangular block. The length is 10.5 cm, the width is 3.22 cm, and the height is 1.5 cm. What is the volume of the block? (Volume = length × width × height). Report your answer with the correct number of significant figures.

Answers

Part 1: How Many Sig Figs?

1. 45.89 4

2. 0.0051 2 (Leading zeros are not significant)

3. 505.0 4 (Captive zero and trailing zero with a decimal are significant)

4. 1,000 1 (Trailing zeros without a decimal are not significant)

5. 1,000. 4 (The decimal makes the trailing zeros significant)

6. 8.50 x 10^3 3 (All digits in scientific notation's coefficient are significant)

Part 2: Calculations with Significant Figures

7. 2.50 g / 0.50 s
   2.50 (3 sig figs) / 0.50 (2 sig figs) = 5. Calculator says 5.
   Final Answer (rounded to 2 sig figs): 5.0 g/s

8. 12.52 m * 1.3 m
   12.52 (4 sig figs) * 1.3 (2 sig figs) = 16.276. Calculator says 16.276.
   Final Answer (rounded to 2 sig figs): 16 m²

9. 100.55 L - 5.1 L
   100.55 (hundredths place) - 5.1 (tenths place). The answer must be rounded to the tenths place.
   Calculator says 95.45.
   Final Answer (rounded to the tenths place): 95.5 L

10. 22.4 g + 1.25 g
    22.4 (tenths place) + 1.25 (hundredths place). The answer must be rounded to the tenths place.
    Calculator says 23.65.
    Final Answer (rounded to the tenths place): 23.7 g

11. (15.2 cm * 3.5 cm) / 2.05 cm
    15.2 (3 sig figs) * 3.5 (2 sig figs) / 2.05 (3 sig figs). The answer is limited by the 2 sig figs in 3.5.
    Calculator says 25.951...
    Final Answer (rounded to 2 sig figs): 26 cm

Challenge Problem

A student measures the sides of a rectangular block. The length is 10.5 cm, the width is 3.22 cm, and the height is 1.5 cm. What is the volume of the block?
Volume = 10.5 cm (3 sig figs) × 3.22 cm (3 sig figs) × 1.5 cm (2 sig figs)
The measurement with the fewest sig figs is 1.5 cm, which has two. The final answer must be rounded to two sig figs.
Calculator says: 50.715 cm³
Final Answer (rounded to 2 sig figs): 51 cm³