Measurement and significant figures – problems and solutions

1. The length of an object measured using a micrometer is 15.08 mm. Determine the significant figures and the number of significant figures.

A. 15.08 mm and three significant figures

B. 1.508 mm and four significant figures

C. 15.08 mm and four significant figures

D. 1.508 mm and three significant figures

Solution :

Significant figures = 15.08 mm

The number of significant figures = 4

The correct answer is C.

2. A student measures the volume of a container using a small cup with a volume of 125 cm^{3}. The container is full after filled with twenty-half cups. Determine the volume of container based on significant figure rules.

A. 2562.5 cm^{3}

B. 2.56 x 10^{3} cm^{3}

C. 2563 cm^{3}

D. 2.56 x 10^{-3} m^{3}

Solution :

Volume of a cup = 125 cm^{3}

Volume of container = 20.5 x 125 cm^{3} = 2562.5 cm^{3}

The correct answer is A.

3. Determine the result of measuring an object as shown in figure below, according to the rules of significant figures.

A. 4.5 mm

B. 4.6 mm

C. 4.6 mm

D. 4.6 mm

Solution :

Main scale = 4.5 mm

Second scale = 11 x 0.01 mm = 0.1 mm (according to the rules of the multiplication of significant figures)

The result of measuring = 4.5 mm + 0.1 mm = 4.6 mm (according to the rules of the summing of significant figures)

The correct answer is C.

**1. Problem:** Round 27.6891 to four significant figures.

**Solution:** 27.69 (because 1 doesn’t affect the third decimal place).

**2. Problem:** If you multiply 6.34 (3 significant figures) by 5.678 (4 significant figures), how many significant figures should your answer have?

**Solution:** The answer should have 3 significant figures.

**3. Problem:** A scientist recorded a result of 5001 grams. How many significant figures does this value have?

**Solution:** 4 significant figures.

**4. Problem:** What is the result when you add 24.5 (3 significant figures) and 1.789 (4 significant figures)?

**Solution:** The sum is 26.289, but considering significant figures, you should round to 26.3.

**5. Problem:** If a physics experiment gives a speed of 0.0056078 m/s, how many significant figures are there?

**Solution:** 5 significant figures.

**6. Problem:** Round 0.007809 to four significant figures.

**Solution:** 0.007809 (because it already has four significant figures).

**7. Problem:** When measuring the depth of a well, you get a value of 78.00 meters. Later, another reading says 78.0001 meters. If you average the values, how many significant figures should your answer have?

**Solution:** The average should have 4 significant figures. Thus, $2+ =78.00005$ becomes 78.00.

**8. Problem:** You measure the width of a book as 150 mm. How many significant figures are there?

**Solution:** 2 significant figures.

**9. Problem:** What is the result when you divide 90.12 (4 significant figures) by 4.0 (2 significant figures)?

**Solution:** The result is 22.53, but considering significant figures, the answer should be rounded to 23.

**10. Problem:** You measure 0.4000 liters of liquid A and 0.4020 liters of liquid B. When reporting the total volume, to how many decimal places should you report your answer?

**Solution:** You should round to 4 decimal places. Thus, $0.4000+0.4020=0.8020$.

**11. Problem:** Round 50.0012 to five significant figures.

**Solution:** 50.001 (because 2 doesn’t affect the fourth decimal place).

**12. Problem:** When subtracting 45.67 (4 significant figures) from 100.1 (4 significant figures), how many significant figures should your answer have?

**Solution:** The answer should have 4 significant figures. So, 100.1 – 45.67 = 54.43.

**13. Problem:** A result was documented as 1020 with no decimal point. How many significant figures does this have?

**Solution:** 3 significant figures.

**14. Problem:** What’s the result when you subtract 2.3456 (5 significant figures) from 5.00 (3 significant figures)?

**Solution:** The result is 2.6544, but considering significant figures, you should round to 2.65.

**15. Problem:** How many significant figures are in the number 0.005002?

**Solution:** 4 significant figures.

**16. Problem:** Round 10.4987 to three significant figures.

**Solution:** 10.5.

**17. Problem:** You get a voltage reading of 50.00 V from one instrument and 50.0005 V from another. If you average the readings, how many significant figures should the result have?

**Solution:** The average should have 4 significant figures. So, $2+ =50.00025$ becomes 50.00.

**18. Problem:** The length of a rod is measured to be 200 mm. How many significant figures does this measurement have?

**Solution:** 1 significant figure.

**19. Problem:** You’re dividing 4.56 (3 significant figures) by 2.0 (2 significant figures). What should be the number of significant figures in the answer?

**Solution:** The answer should have 2 significant figures. So, 4.56 ÷ 2.0 = 2.28.

**20. Problem:** The measured distance between two towns is 100.50 km. How many significant figures does this measurement have?

**Solution:** 5 significant figures.