Least count and significant figures - Question Bank

1. What is the least count of a digital balance that displays readings to two decimal places (e.g., 12.34 g)?
A) 1 g
B) 0.1 g
C) 0.01 g
D) 0.001 g
2. The result of 10.2 m + 3.45 m - 1.0 m, expressed with the correct number of significant figures, is:
A) 12.65 m
B) 12.7 m
C) 12.6 m
D) 13 m
3. Which of the following numbers has exactly 4 significant figures?
A) 12345
B) 10000
C) 1.200 x 10^3
D) 0.0012
4. What is the least count of a screw gauge if its pitch is 0.5 mm and it has 50 divisions on its circular scale?
A) 0.5 mm
B) 0.01 mm
C) 0.05 mm
D) 1 mm
5. When rounding off the number 2.465 to three significant figures, the result is:
A) 2.46
B) 2.47
C) 2.50
D) 2.465
6. How many significant figures are in 1.00000?
A) 1
B) 3
C) 6
D) 7
7. The least count of a measuring instrument determines the:
A) Absolute error
B) Relative error
C) Minimum measurable value
D) Maximum measurable value
8. If a measurement is reported as 15.0 cm, it implies the true value lies between:
A) 14.9 cm and 15.1 cm
B) 14.5 cm and 15.5 cm
C) 14.0 cm and 16.0 cm
D) 15.00 cm and 15.01 cm
9. What is the result of 5.678 / 2.3, with the correct number of significant figures?
A) 2.4686
B) 2.47
C) 2.5
D) 2.46
10. How many significant figures are in the number 0.000000001?
A) 0
B) 1
C) 9
D) 10
11. The precision of a measurement is directly related to its:
A) Magnitude
B) Least count
C) Accuracy
D) Range
12. What is the least count of a meter scale divided into 100 equal parts?
A) 1 cm
B) 1 mm
C) 0.1 cm
D) 0.01 cm
13. The number of significant figures in 1010 is:
A) 2
B) 3
C) 4
D) Ambiguous
14. A measuring instrument has a least count of 0.001 mm. This implies it can measure lengths with an uncertainty of:
A) 0.1 mm
B) 0.01 mm
C) 0.001 mm
D) 1 mm
15. What is the result of 2.5 x 10^3 + 1.2 x 10^2, with the correct number of significant figures?
A) 3.7 x 10^3
B) 2.62 x 10^3
C) 2.6 x 10^3
D) 3700
16. What is the result of 7.25 - 3.1, with the correct number of significant figures?
A) 4.15
B) 4.2
C) 4.1
D) 4
17. How many significant figures are in the number 500.0?
A) 1
B) 2
C) 3
D) 4
18. What is the rule for significant figures when dealing with exact numbers (like counts)?
A) They have one significant figure.
B) They have as many significant figures as the other measured values.
C) They are considered to have an infinite number of significant figures.
D) They have two significant figures.
19. If a vernier caliper has a least count of 0.01 cm, what is the minimum difference it can measure?
A) 0.01 cm
B) 0.1 cm
C) 1 cm
D) 0.001 cm
20. Which of the following represents the smallest uncertainty?
A) 10.0 +/- 0.1
B) 10.00 +/- 0.01
C) 10 +/- 1
D) 10.000 +/- 0.001
21. When measuring the length of an object with a ruler marked in centimeters, if the object measures between 15 cm and 16 cm, and you estimate it to be 15.7 cm, the digit '7' represents:
A) A precisely known digit.
B) An uncertain digit.
C) A leading zero.
D) A trailing zero.
22. The number of significant figures in 0.02030 is:
A) 3
B) 4
C) 5
D) 2
23. In a measurement of 25.37 +/- 0.02 cm, what is the least count of the instrument used?
A) 25.37 cm
B) 0.02 cm
C) 1 cm
D) 0.1 cm
24. What is the least count of a thermometer with markings every 0.5 degrees Celsius?
A) 1 degree C
B) 0.5 degrees C
C) 0.1 degrees C
D) 0.05 degrees C
25. How many significant figures are in 150.050?
A) 4
B) 5
C) 6
D) 7
26. What is the rule for rounding off a digit when the next digit is exactly 5?
A) Always round up.
B) Always round down.
C) Round to the nearest even digit.
D) Round to the nearest odd digit.
27. Which of the following measurements has the highest number of significant figures?
A) 10.00 kg
B) 1.000 kg
C) 0.100 kg
D) 10 kg
28. The least count of a device indicates its:
A) Accuracy
B) Range
C) Precision
D) Resolution
29. If the vernier scale of a caliper has 50 divisions and it coincides with 49 main scale divisions, with 1 MSD = 1 mm, what is the least count?
A) 0.02 mm
B) 0.01 mm
C) 0.05 mm
D) 0.1 mm
30. A measuring tape has markings every millimeter. What is its least count?
A) 1 cm
B) 0.1 cm
C) 1 m
D) 0.01 cm
31. What is the result of 10.5 g / 3.0 g, expressed with the correct number of significant figures?
A) 3.5 g
B) 3.50 g
C) 3 g
D) 4 g
32. What is the result of 4.5 m x 2.1 m, expressed with the correct number of significant figures?
A) 9.45 m^2
B) 9.5 m^2
C) 9 m^2
D) 9.4 m^2
33. What is the result of 2.5 cm + 1.35 cm, expressed with the correct number of significant figures?
A) 3.85 cm
B) 3.9 cm
C) 3.8 cm
D) 4 cm
34. Express 0.0000123 in scientific notation with 3 significant figures.
A) 1.23 x 10^-5
B) 1.23 x 10^5
C) 1.2 x 10^-5
D) 1.230 x 10^-5
35. How many significant figures are in the number 7.00 x 10^4?
A) 1
B) 2
C) 3
D) 4
36. How many significant figures are in the number 300?
A) 1
B) 2
C) 3
D) Ambiguous
37. How many significant figures are in the number 120.05?
A) 3
B) 4
C) 5
D) 6
38. How many significant figures are in the number 0.0056?
A) 1
B) 2
C) 3
D) 4
39. When adding or subtracting two quantities, the result should have the same number of decimal places as the quantity with the:
A) Most significant figures.
B) Least significant figures.
C) Most decimal places.
D) Least decimal places.
40. When multiplying or dividing two quantities, the result should have the same number of significant figures as the quantity with the:
A) Most significant figures.
B) Least significant figures.
C) Most decimal places.
D) Least decimal places.
41. Zeros between two non-zero digits are:
A) Never significant.
B) Always significant.
C) Significant only if they are at the beginning of the number.
D) Significant only if they are at the end of the number.
42. Trailing zeros in a number without a decimal point are:
A) Always significant.
B) Never significant.
C) Ambiguous and their significance cannot be determined without further information.
D) Significant only if they are part of a scientific notation.
43. Trailing zeros (zeros to the right of the last non-zero digit) in a number with a decimal point are:
A) Never significant.
B) Always significant.
C) Significant only if they are before the decimal point.
D) Significant only if they are after the decimal point.
44. Leading zeros (zeros to the left of the first non-zero digit) are:
A) Always significant.
B) Never significant.
C) Significant only if they are after a decimal point.
D) Significant only if they are part of a scientific notation.
45. Which of the following is a non-zero digit and is always significant?
A) 0
B) 1
C) 10
D) 100
46. What does 'significant figures' in a measurement represent?
A) All the digits in a measurement, including uncertain ones.
B) Only the digits that are exactly known.
C) The digits that are known with certainty plus one doubtful digit.
D) The number of decimal places in a measurement.
47. In a screw gauge, the main scale is calibrated in millimeters and the circular scale has 100 divisions. If one main scale division is 1 mm, what is its least count?
A) 1 mm
B) 0.1 mm
C) 0.01 mm
D) 0.001 mm
48. A vernier caliper has 10 vernier scale divisions coinciding with 9 main scale divisions. If one main scale division is 1 mm, what is the least count of the vernier caliper?
A) 0.1 mm
B) 0.01 mm
C) 1 mm
D) 0.09 mm
49. Which of the following statements best describes the significance of the least count?
A) It determines the precision of the instrument.
B) It determines the accuracy of the instrument.
C) It is always equal to the main scale division.
D) It is independent of the number of divisions on the vernier scale.
50. What is the least count of a measuring instrument?
A) The maximum possible error in a measurement.
B) The smallest value that can be measured accurately by the instrument.
C) The total range of the instrument.
D) The number of divisions on the main scale.
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