Significant Figures - UNSOLVED PRACTICE SET

Q7. State the rules for determining the number of significant figures in a given number. Illustrate with two examples.

Q8. What are the rules for rounding off numbers to a given number of significant figures? Explain with examples.

Q9. A student measures the length of a room as 5.2 m and the breadth as 3.45 m. How many significant figures should the calculated area have? Explain your reasoning.

Q10. In your school lab, you measure the diameter of a coin as 2.45 cm using a vernier caliper. Your friend measures the same coin with a metre scale and records 2.5 cm. Which measurement is more precise, and how does this reflect in the significant figures?

Q11. Explain why the zeros in the number 0.00203 are significant or not significant. Identify all significant figures in this number.

Q12. Distinguish between accuracy and precision. How do significant figures help in expressing the precision of a measurement?

Q13. Explain the concept of significant figures with examples. Discuss all the rules for counting significant figures, including the special cases of zeros, exact numbers, and numbers in scientific notation.

Q14. Describe the rules for arithmetic operations with significant figures:

(i) Addition and subtraction

(ii) Multiplication and division

(iii) Powers and roots

Illustrate each rule with a numerical example.

Q15. A student measures the length of a rectangular field as 125.3 m and the breadth as 45.2 m. Another student measures the same field and records length as 125 m and breadth as 45 m. Analyse the difference in precision between these two sets of measurements. Calculate the area in both cases and discuss how significant figure rules affect the final reported area.

Q16. Perform the following calculations and express the results with the correct number of significant figures:

(a) 12.34 + 1.2 + 0.123

(b) 4.56 × 2.1

(c) 100.0 ÷ 3.00

(d) (2.5)³

(e) 9.80 − 9.72

Q17. In a school experiment, a student measures the following:

Mass of a body: 250.0 g

Volume of the body: 50.0 cm³

Time for 10 oscillations: 20.0 s

(a) Calculate the density of the body and express it with the correct number of significant figures.

(b) Calculate the time period of one oscillation and express it with correct significant figures.

(c) If the student measures the length of a pendulum as 100.0 cm, calculate g using T = 2π√(L/g) and express the result with appropriate significant figures.

Q18. A physics teacher gives three students the same task: measure the thickness of a single sheet of paper from a 500-page notebook.

Student A counts 500 sheets, measures the total thickness as 4.5 cm, and calculates the thickness of one sheet.

Student B counts 250 sheets, measures the total thickness as 2.25 cm, and calculates.

Student C counts 100 sheets, measures the total thickness as 0.90 cm, and calculates.

(a) Calculate the thickness of one sheet reported by each student.

(b) How many significant figures does each result have?

(c) Which student's method gives the most precise result, and why?

(d) What does this experiment teach you about improving precision in measurement?