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© 2009 Chung Tai Educational Press. All rights reserved.

1. Choose suitable measuring units from the brackets for the measurement of the following.

[ mm, cm, m, km, cm2, m2, mg, g, kg, mL, L ]

(a) The weight of a packet of potato chips

(b) The thickness of a mobile phone

(c) The capacity of a bathtub

(d) The area of an A4 paper

(e) The weight of an adult

(f) The length of a highway

2. Choose suitable measuring tools from the brackets for the measurement of the following.

[ Vernier caliper, measuring tape, spoon, beaker, balance, bathroom scale, thermometer, electronic timer, clock ]

(a) The temperature of water

(b) The width of a wardrobe

(c) The weight of a cup of rice

(d) The capacity of a jar of milk

(e) The thickness of an SD memory card

(f) The time required to swim 50 m

3. Determine whether the units and degree of accuracy in the following statements are appropriate. If not, try to make necessary corrections.

(a) The capacity of this can of lemon tea is 340 mL.

(b) The length of the Yellow River is 5 464 000 000 mm.

(c) The weight of this notebook computer is 2.398 7 kg.

(d) Sunny completed a race in 0.004 1 hour.

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4. (a) Referring to the clock in the figure, write down the time displayed.

1211

10

9

8

7 5

4

3

1

2

6

(b) Find the degree of accuracy in the measurement.

5. (a) Referring to the thermometer in the figure, write down the temperature measured.

94 6 8 100 2 4 6 108°F

(b) Find the degree of accuracy in the measurement.

6. In the figure, three rulers with different scale intervals are used to measure line segment AB.

A B A B A B

0cm

1 2 3 41 2 3 40cm

0cm

1 2 3 4

Ruler I Ruler II Ruler III

(a) (i) Referring to ruler I, write down the length of line segment AB.

(ii) Referring to ruler II, write down the length of line segment AB.

(iii) Referring to ruler III, write down the length of line segment AB.

(b) Which ruler is the most precise one?

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7. In the figure, the volume of water inside cylinders I, II and III are the same.

40 cm3

30 cm3

20 cm3

10 cm3

40 cm3

30 cm3

20 cm3

10 cm3

40 cm3

30 cm3

20 cm3

10 cm3

Cylinder I Cylinder II Cylinder III

(a) Which cylinder do you think should be used to measure the volume of water more accurately?

(b) According to the cylinder chosen in (a), write down the volume of water.

8. It is known that the patterns in Figure I and Figure II are identical, and the areas of each square in Figure I and Figure II are

2cm 25.0 and 2cm 1 respectively.

Figure I Figure II

(a) Which figure do you think should be used to measure the area of the pattern more accurately?

(b) According to the figure chosen in (a), measure the area of the pattern.

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9. The figure shows a plot to be developed by the government. The plot will be developed into three regions, including a residential area, an open space and a shopping centre.

Residential area

Open space

Shopping centre

20 m

20 m

Marco is going to use one of the following methods to measure the area of the plot.

Method 1: Measure the area of each region, then find the sum of the areas of the three regions.

Method 2: Measure the area of the whole plot directly.

(a) Which method do you think should be used to measure the area of the plot more accurately?

(b) According to the method chosen in (a), measure the area of the plot.

10. Joyce wants to measure the weight of a 2A battery. She collects 5 identical 2A batteries and weighs them on a spring balance. The result is 120 g.

(a) According to Joyce’s method, what is the weight of a 2A battery?

(b) Suggest a method to measure the weight of a 2A battery more accurately.

11. Suggest a method to measure the thickness of an Octopus card. (List the tools required and the measuring procedures.)

12. Suggest a method to measure the volume of a $1 coin. (List the tools required and the measuring procedures.)

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13. It is given that the length of the curve AB in the figure is 2.5 cm. Using this as a benchmark, estimate the length of the curve AC.

A C

B

14. It is given that the area of the circle in the figure is 12 cm2. Using this as a benchmark, estimate the area of the shaded region.

15. It is given that the capacity of the glass in the figure is 240 mL. Using this as a benchmark, estimate the volume of water in the glass.

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16. It is given that the line spacing of the single line paper in the figure is 7 mm. Estimate the length of the single line paper and illustrate the estimation strategy used.

Length

NO.

DATE

17. Estimate the number of decimal places of the following value and illustrate the estimation strategy used.

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18. Heidi creates a picture with some circles. Estimate the number of circles in the picture using the decomposition-recomposition strategy.

19. Estimate the number of candies in the photo and illustrate the estimation strategy used.

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20. The following figure shows the floor plan of a cabin. Estimate the number of seats in the cabin and illustrate the estimation strategy used.

Each represents a seat.

21. The figure shows an extract from a passage.

(a) Estimate the number of words in the extract and illustrate the estimation strategy used.

(b) If the extract is about 31

of the whole passage,

estimate the number of words in the whole passage.

Several cases of a new type of flu infection have been confirmed in this city. How well do you know this type of flu?

Symptoms The symptoms of this type of flu include fever, lethargy, loss of appetite and coughing. Some may also have a runny nose, sore throat, vomiting and diarrhoea.

Mode of transmission This type of flu is mainly spread among people through coughing and sneezing. Besides, people may also become infected if they touch their nose or mouth after touching objects with flu viruses.

Prevention • Wash hands properly to keep them clean.

Avoid touching mouth, nose and eyes. • Cover nose and mouth when sneezing or

coughing. Wash hands with liquid soap immediately after sneezing or coughing.

• Keep the environment clean. Do not spit. Wrap respiratory discharges with tissue paper, and dispose it in a rubbish bin with lid.

• Wear a mask whenever flu symptoms are developed. See a doctor right away and do not go to work or school.

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22. The figure shows a collapsed brick wall.

Height

Length

20 cm

Given that the figure is drawn to scale and the length of each brick is 20 cm,

(a) estimate the length of the brick wall and illustrate the estimation strategy used.

(b) estimate the height of the brick wall and illustrate the estimation strategy used.

23. Find the maximum absolute error of each of the following approximate values, and the upper limit and lower limit of its actual value.

(a) 156 mL (corr. to the nearest mL)

(b) $20 (corr. to the nearest $10)

(c) 0.001 g (corr. to 1 sig. fig.)

(d) 70.0 km (corr. to 3 sig. fig.)

24. Find the maximum absolute error of each of the following approximate values, and the range of its actual value.

(a) 800 kg (corr. to the nearest 100 kg)

(b) 800 kg (corr. to 2 sig. fig.)

(c) 800 kg (corr. to 3 sig. fig.)

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25. Find the maximum absolute error, relative error (in the form of n1 ) and percentage error of each of the

following approximate values. (Give your answers correct to 3 significant figures if necessary.)

(a) $500 000 (corr. to the nearest $1 000)

(b) 290 L (corr. to the nearest 10 L)

(c) 47 cm2 (corr. to 2 sig. fig.)

(d) 22.8 s (corr. to 3 sig. fig.)

26. Frankie measures the time taken by him to finish a composition and the result is 59 minutes, correct to the nearest minute.

(a) Find the maximum absolute error of the time measured.

(b) Find the relative error of the time measured in the form of

n1 .

(c) Find the percentage error of the time measured. (Give your answer correct to 3 significant figures.)

27. Samantha measures the length of a rope and the result is 3.12 m, correct to 3 significant figures.

(a) Find the maximum absolute error of the length measured.

(b) Find the relative error of the length measured in the form of n1 .

(c) Find the percentage error of the length measured. (Give your answer correct to 3 significant figures.)

28. Mandy rounds off the selling price $9.9 of an item to $10.

(a) Find the absolute error of the approximate value.

(b) Find the relative error of the approximate value in the form of

n1 .

(c) Find the percentage error of the approximate value. (Give your answer correct to 3 significant figures.)

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29. Vincent measures the capacity of a water tank and the result is 45 L. If the relative error of the

measurement is

151 , find the range of the actual capacity of the water tank.

30. Samuel measures the weight of a letter and the result is 55 g. If the percentage error of the measurement is 0.04%, find the range of the actual weight of the letter.

31. Phoebe measures the length of a pencil with a ruler as follows.

0

cm1 2 3 4 5 6 7 98 10

(a) Referring to the figure, write down the length of the pencil.

(b) Find the maximum absolute error of the length measured.

(c) Find the range of the actual length of the pencil.

(d) Find the relative error of the length measured in the form of

n1 .

(e) Find the percentage error of the length measured. (Give your answer correct to 3 significant figures.)

32. An equilateral triangle has sides of 6.6 cm each, correct to 2 significant figures.

(a) Find the upper and lower limits of the actual length of each side of the equilateral triangle.

(b) Find the upper and lower limits of the actual perimeter of the equilateral triangle.

(c) Is it possible for the actual perimeter of the equilateral triangle to be 20 cm? Explain briefly.

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33. (a) Vivian weighs a piece of chocolate on a spring balance and the result is 5 g, correct to the nearest g. Find the percentage error of the measurement.

(b) Yendy weighs 20 pieces of identical chocolate on the same spring balance and the result is 100 g.

(i) Find the upper and lower limits of the actual total weight of the 20 pieces of chocolate.

(ii) If Yendy calculates the weight of a piece of chocolate based on the total weight of the 20 pieces of chocolate, find the upper and lower limits of the actual weight of a piece of chocolate, and the maximum absolute error of the weight of a piece of chocolate.

[ Hint: Maximum absolute error

2limitLower limitUpper −

= ]

(iii) What is the percentage error of the weight of a piece of chocolate found by Yendy?

(c) Comparing the results of (a) and (b), whose method should be used to measure the weight of a piece of chocolate more accurately? Explain briefly.

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