Maths Approximation and Errors 數學近似值&錯誤(20分)

1. How many significant figures are there in the number 0.001 203 00?
答案：C
在小數中，有效數字的位數，在小數左方的零是不計位數的

0.001 203 00由小數第三個非零數字 1 數起，加上其後的 0 有六位，所以為六位有數字

2. Round off 80 652 037, correct to 3 significant figures.
答案：D
從左方的第三位有效數字是6，由於第四位數字是5，故應該四捨五入


3. Round off –0.091 998 72, correct to 4 significant figures.
答案：C
從左方的第四位有效數字是9，由於第五位數字是8，故應該四捨五入


4. How many significant figures are there in the number 1 234 000 (cor. to the nearest ten)?
答案：B

5. Express as decimal correct to 3 significant figures.
A. 0.538
B. 0.539
C. 1.53
D. 1.54
7. Paul rides a bicycle to finish a track in 2 minutes 52 seconds. Change the unit of that time to minutes and correct the answer to 3 significant figures.
答案：A
8. It takes a train 1 day 6 hours and 46 minutes to complete a journey. Change the unit ot that time to hours and correct the answer to 3 significant figures.
答案：B
9. The volume of a cylinder is measured to be 635 cm3, correct to the nearest cm3. Find the maximum error of this measurement.
答案：D
1/2×1 cm3 = 0.5 cm3

10. The weight of an earring is 5.07 g, correct to the nearest 0.01 g. What is the relative error of this measurement? (Give the answer correct to 2 significant figures.)
答案：C

maximum error
=1/2×0.01 g = 0.005 g
relative error
=0.005 / 5.07 = 0.0009861932939

11. The temperature reading on a thermometer is 65.2 ℃, correct to the nearest 0.2 ℃. Find the percentage error of this measurement. (Give the answer correct to 2 significant figures.)
答案：A

maximum error
=1/2×0.2 ℃ = 0.1℃
relative error
=0.1 / 65.2 ×100% = 0.15%

12. The speed of a car is measured to be 85.5 km/h and the percentage error is . Find the maximum error of this measurement.
答案：D

13. Sam measures the capacity of a flask to be 1 250 mL and the relative error is 0.002. Find the upper limit of the actual capacity of the flask.
答案：B
maximum error
=1 250×0.002 = 2.5
upper limit = 1 250+2.5 = 1252.5 mL

14. Kelly measures the area of a poster to be 1 180 cm2 and the percentage error is . Find the lower limit of the actual area of the poster.
答案：B

maximum error
=10×1/2 = 5cm2
upper limit = 1 180 - 5 = 1175 mL

15. In an experiment, it is found that the actual temperature of a solution lies between 75.4 ℃ and 75.8 ℃. What is the relative error of this measurement? (Give the answer correct to 2 significant figures.)
答案：A
16. It is given that the actual width and length of a rectangle are 8.52 cm and 15.49 cm respectively. Round off the actual width and length of the rectangle correct to the nearest integer, and then estimate its perimeter.
A. 46 cm
B. 48 cm
C. 120 cm
D. 135 cm
17. The time taken by Thomas to answer a set of M.C. questions is measured to be 1 minute 21 seconds and the error is at most 1 second. What is the percentage error of this measurement? (Give the answer correct to the nearest 0.01%.)
A. 1.23%
B. 0.83%
C. 0.62%
D. 0.41%
18. Peter wants to know the thickness of a piece of CD by first measuring the thickness of 10 pieces of CDs to be 14 mm (correct to the nearest mm) and then dividing his measured value by the total number of pieces of CDs. Find the relative error, correct to the nearest 0.01.
A. 0.36
B. 0.35
C. 0.18
D. 0.04
19. It is given that the length of a square is measured to be 4.6 cm, correct to the nearest 0.2 cm. Find the upper limit of the area of the square.
A. 23.04 cm2
B. 22.09 cm2
C. 21.16 cm2
D. 20.25 cm2
20. It is known that the base area and the height of a prism are measured to be 80 cm2 and 5.2 cm respectively. If all measurements are correct to 2 significant figures, what is the lower limit of the volume of the prism?
A. 402.9 cm3
B. 405.45 cm3
C. 406.85 cm3
D. 409.425 cm3

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