Measurements

Physics, HSSC-KPK First Year. This chapter is split into 49 topics and has 1,180 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Physics Scope, SI Base Units & Derived Units 24 questions
2. Supplementary Units: Radian & Steradian 22 questions
3. Scientific Notation, Prefixes & Non-SI Units 22 questions
4. Writing Unit Symbols & Names 20 questions
5. Errors: Systematic, Random & Least Count 22 questions
6. Uncertainties: Absolute, Relative & Propagation Rules 26 questions
7. Significant Figures: Rules & Calculations 24 questions
8. Precision vs Accuracy 20 questions
9. Dimensions: Fundamental & Derived Dimensions 22 questions
10. Dimensional Analysis: Variables, Constants, Formula & Applications 24 questions
11. Radian Measure: Arc Length and Radius Numericals 25 questions
12. Degree and Radian Conversion Numericals 25 questions
13. Steradian and Solid Angle Numericals 21 questions
14. Scientific Notation: Writing and Reading Numbers 23 questions
15. Scientific Notation Arithmetic and Powers 24 questions
16. SI Prefix Conversion to Base Units 25 questions
17. Converting Between SI Prefixes and Units 25 questions
18. SI Prefix Names, Symbols and Multipliers 27 questions
19. Light Year, Angstrom and Micron Numericals 24 questions
20. Absolute, Relative and Percent Uncertainty Conversions 25 questions
21. Uncertainty in Sums and Differences of Measurements 24 questions
22. Uncertainty in Products and Quotients 25 questions
23. Uncertainty in Powers and Roots of Measured Quantities 25 questions
24. Uncertainty in Physical Formulae: Combined Applications 26 questions
25. Least Count, Resolution and Zero Error Numericals 26 questions
26. Quoting Measurements as Best Estimate Plus or Minus Uncertainty 23 questions
27. Counting Significant Figures in Measured Values 30 questions
28. Significant Figures: Zeros, Decimal Points and Scientific Notation 30 questions
29. Identifying Numbers by Their Number of Significant Figures 25 questions
30. Rounding Numbers to a Given Number of Significant Figures 25 questions
31. Rounding Measured and Calculated Values to the Right Precision 25 questions
32. Significant Figures in Addition and Subtraction of Measurements 25 questions
33. Rounding the Sum or Difference of Measured Quantities 25 questions
34. Significant Figures in Multiplication and Division 25 questions
35. Rounding Products and Quotients of Measured Quantities 25 questions
36. Precision of a Recorded Measurement: Position of the Last Digit 25 questions
37. Comparing the Precision of Different Recorded Values 25 questions
38. Interpreting Repeated Readings as Accurate, Precise or Both 25 questions
39. Dimensional Formulas of Derived Quantities 25 questions
40. Expressing Derived Quantities in SI Base Units 25 questions
41. Identifying Physical Quantities from Their Dimensions 21 questions
42. Checking Dimensional Homogeneity of Equations 25 questions
43. Dimensions of the Two Sides of an Equation 25 questions
44. Deriving Possible Formulae by Dimensional Analysis 25 questions
45. SI Conventions for Writing Unit Symbols and Names: Applications 20 questions
46. Classifying Errors in Practical Measurements 21 questions
47. Accuracy and Precision: Reasoning Questions 22 questions
48. Uses and Limitations of Dimensional Analysis 22 questions
49. Physical Quantities, Systems of Units and Scientific Reasoning 20 questions

Sample questions: Measurements

10 sample questions with the correct answer and an explanation. Try to answer each one before reading the explanation.

Q1. Count the significant figures in 2.1000 × 10⁴ kg.

• A. 7
• B. 4
• C. 5(correct answer)
• D. 6

Answer: C.Applying the rules: in scientific notation only the digits of the mantissa are counted; zeros to the right of the decimal point after a non-zero digit are significant; therefore 2.1000 × 10⁴ has 5 significant figures.

Q2. The measured value 1.60 × 10⁻¹⁹ has how many significant figures?

• A. 4
• B. 3(correct answer)
• C. 2
• D. 5

Answer: B.Applying the rules: in scientific notation only the digits of the mantissa are counted; zeros to the right of the decimal point after a non-zero digit are significant; therefore 1.60 × 10⁻¹⁹ has 3 significant figures.

Q3. The measured value 0.1010 N has how many significant figures?

• A. 3
• B. 4(correct answer)
• C. 5
• D. 6

Answer: B.Applying the rules: zeros to the left of the first non-zero digit are not significant; zeros to the right of the decimal point after a non-zero digit are significant; zeros between non-zero digits are significant; therefore 0.1010 has 4 significant figures.

Q4. Count the significant figures in 4.500 × 10³ A.

• A. 5
• B. 6
• C. 4(correct answer)
• D. 3

Answer: C.Applying the rules: in scientific notation only the digits of the mantissa are counted; zeros to the right of the decimal point after a non-zero digit are significant; therefore 4.500 × 10³ has 4 significant figures.

Q5. Count the significant figures in 0.02030 m.

• A. 4(correct answer)
• B. 6
• C. 5
• D. 3

Answer: A.Applying the rules: zeros to the left of the first non-zero digit are not significant; zeros to the right of the decimal point after a non-zero digit are significant; zeros between non-zero digits are significant; therefore 0.02030 has 4 significant figures.

Q6. A reading of 8.0 × 10⁻⁵ kg is recorded. How many of its digits are significant?

• A. 3
• B. 1
• C. 4
• D. 2(correct answer)

Answer: D.Applying the rules: in scientific notation only the digits of the mantissa are counted; zeros to the right of the decimal point after a non-zero digit are significant; therefore 8.0 × 10⁻⁵ has 2 significant figures.

Q7. Count the significant figures in 0.00708600.

• A. 9
• B. 5
• C. 6(correct answer)
• D. 7

Answer: C.Applying the rules: zeros to the left of the first non-zero digit are not significant; zeros to the right of the decimal point after a non-zero digit are significant; zeros between non-zero digits are significant; therefore 0.00708600 has 6 significant figures.

Q8. A reading of 3.600 × 10⁻² is recorded. How many of its digits are significant?

• A. 4(correct answer)
• B. 6
• C. 3
• D. 5

Answer: A.Applying the rules: in scientific notation only the digits of the mantissa are counted; zeros to the right of the decimal point after a non-zero digit are significant; therefore 3.600 × 10⁻² has 4 significant figures.

Q9. A reading of 1.0 × 10⁻⁶ is recorded. How many of its digits are significant?

• A. 1
• B. 3
• C. 2(correct answer)
• D. 4

Answer: C.Applying the rules: in scientific notation only the digits of the mantissa are counted; zeros to the right of the decimal point after a non-zero digit are significant; therefore 1.0 × 10⁻⁶ has 2 significant figures.

Q10. Which number below is quoted with exactly 4 significant figures?

• A. 8.0 × 10⁻⁵
• B. 0.02030(correct answer)
• C. 0.3
• D. 1.60 × 10⁻¹⁹

Answer: B.0.02030 has 4 significant figures (zeros to the left of the first non-zero digit are not significant; zeros to the right of the decimal point after a non-zero digit are significant; zeros between non-zero digits are significant); the others have 3, 1, 2.