Practice Problems: Measurement Solutions

1. How many significant figures are in the number 0.00305?
Three significant figures. The zeroes are all placeholders.

2. Round 3.14159 to 3 significant figures.
3.14

3. What is the result of 12.3 + 5.67 when expressed with the correct number of significant figures?
18.0
Round off to the tenths place because 12.3 is only significant to the tenths place.

4. Multiply 2.5 x 3.20. Express your answer using the correct number of significant figures.
8.0
Round off to two significant figures because 2.5 has only two significant figures.

5. How many significant figures are in 1.000 x 10³?
Four significant figures. Zeroes that aren't placeholders are significant.

6. Express the sum of 1.23 x 10⁵ and 4.5 x 10⁴ in scientific notation with the correct number of significant figures.
1.23 x 10⁵ = 123000 is significant to the ten-thousands place
4.5 x 10⁴ = 45000 is significant to the thousands place
The answer must be rounded to the thousands place
168000 = 1.68 x 10⁵

7. What is the result of 0.0085/2.1? Express your answer with the correct number of significant figures.
0.0040
Round off to two significant figures because each of the numbers in the division have two significant figures.

8. How many significant figures are in 10,000 when it's written as an exact number?
Exact numbers have infinite significant figures.

9. Add 102.3 + 5.67 + 0.1. Express your result with the appropriate number of significant figures.
108.1
Round off to the tenths place because 102.3 and 0.1 only have significance to the tenths place. 

10. Convert 0.0350 km to meters, expressing your answer with the correct number of significant figures.
0.0350 km (1000 m/km) = 35.0 m
Round to three significant figures

11. Calculate the area of a rectangle with length 4.56 cm and width 3.2 cm. Express your answer with the correct number of significant figures.
Length: 4.56 cm (3 sig figs)
Width: 3.2 cm (2 sig figs)
Area = 4.56 cm × 3.2 cm = 14.592 cm²
The result should have 2 sig figs (limited by the least precise measurement), so the final answer is 14.6 cm².

12. A cylindrical tank has a diameter of 1.50 m and a height of 3.0 m. Calculate its volume in cubic meters, expressing your answer with the correct number of significant figures. (Use π = 3.14)
Diameter: 1.50 m (3 sig figs)
Height: 3.0 m (2 sig figs)
π is given as 3.14 (3 sig figs)
Volume = π × (diameter/2)² × height
V = 3.14 × (0.75 m)² × 3.0 m = 5.2965 m³
The result should have 2 sig figs (limited by the height), so the final answer is 5.3 m³.

13. You are given a rectangular wooden block and a metric ruler marked in millimeters. This means that the ruler's smallest division is 1 mm. You then measure the length, width, and height of the block using the ruler and record each measurement with the appropriate number of significant figures.
Length: 37.5 mm Width: 25.0 mm Height: 12.5 mm
a. Calculate the volume of the block using your measurements. Express the final answer with the correct number of significant figures.
Volume calculation: V = 37.5 mm × 25.0 mm × 12.5 mm = 11,718.75 mm³
Rounding to 3 significant figures (limited by our measurements):
11,700 mm³ or 11.7 cm³
b. The density of a substance is defined as being its mass divided by its volume. If the mass of the block is measured to be 15.23 g, calculate the density of the wood. Express your answer with the appropriate number of significant figures and units.
Density calculation: Density = Mass / Volume = 15.23 g / 11.7 cm³ = 1.30171... g/cm³
Rounding to 3 significant figures (limited by the volume measurement):  Density = 1.30 g/cm³

Textbook Assignment:
Find the solutions in the Student Solutions Guide. Click here.

1. Answer question 17 in the Concept Items section of the Chapter Review for Chapter 1.

2. Answer questions 29, 29, and 35 in the Critical Thinking Items section of the Chapter Review for Chapter 1.