1. (a) Round off each of the following numbers to the nearest integer.
(i) 4.2
(ii) 2.8
(iii) 9.3
(iv) 3.5
(b) Hence estimate the value of 4 .
2

2 .
8

9 .
3

3 .
5 .
2.
(a) Find a clustered value to represent all of the following number s.
492, 527, 511, 499, 484
(b) Hence estimate the value of 492

527

511

499

484 .
3.
Complete the following.
(a) When we estimate the value of 59

0 .
compatible values for estimation will obtain
26 , since
59

0 .
26

59
 and 0

.
26


.
, using
(b) When we estimate the value of 601 .
2

2 .
9 , since compatible values for estimation will obtain 601 .
2

2 .
601 .
2

9
  and 2 .
9


.
, using
4.
Estimate the values of the following expressions and state the strategies used.
(a) 593

119

204

175

682

123

287
(b)

2 .
17

1 .
89

2 .
03

1 .
95

1 .
92

2 .
08

2 .
11

1 .
96
(c) 39 .
823

0 .
491
1.5
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2009 Chung Tai Educational Press. All rights reserved.

5.
Estimate the values of the following expressions and state the strategies used.
(a) 1 322

4 .
9
(b) 279 .
2

5 .
03
(c) 4 408 .
72

8 .
1
6.
Estimate the values of the following expressions and state the strategies used.
(a) 65

( 30 .
9

13 )
(b) 730

2 .
998

0 .
303
(c) 9 .
01

( 278 .
9

63 .
2 )
7. Determine whether the following expressions are reasonable.
(a) 19 .
23

10 .
19

28 .
71

69 .
24

11 .
54

1 .
49

60
(b) 0 .
252

4 .
86

201 .
9

100
(c) ( 124 .
88

3 .
9

5 .
009

19 .
7 )

0 .
333

600
8.
Consider the following expression.
5 673 .
2

8 703 .
1

9 400 .
3

1 925 .
4

4 029 .
5
(a) Estimate whether the result of the expression is less than 32 000 by rounding up.
(b) Estimate whether the result of the expression is greater than 26 000 by rounding down.
9.
Edwin buys an electrical appliance with a marked price of $999 at a discount of 20%. Estimate the amount paid by Edwin and state the strategy used.
10.
The selling prices of Piyo shampoo and Piyo conditioner are $34.9 and $29.9 per bottle respectively.
Estimate the total selling price of 4 bottles of Piyo shampoo and 3 bottles of Piyo conditioner, and state the strategy used.
1.6
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2009 Chung Tai Educational Press. All rights reserved.

11.
Rachel is going to withdraw some money from an ATM to buy five books at $77.5, $126, $115, $109.5 and $118. Estimate whether withdrawing a $500 banknote is enough for Rachel to buy the books required. Explain briefly.
12. Peggy is going to buy 6 bars of chocolate for $7.9 each from a supermarket. If a stamp will be given for every purchase of $50, estimate whether Peggy can receive a stamp. Explain briefly.
13. The figure shows trapezium ABCD .
A 6.13 cm B
4.92 cm 4.8 cm 4.92 cm
D 8.29 cm C
(a) Estimate the perimeter of trapezium ABCD and state the strategy used.
(b) William claimed that the area of trapezium ABCD is about 70 cm
2
. Determine whether his estimation is reasonable.
14. Steven Chicken Soup in packs of 298 mL and 500 mL are sold at $7.5 and $9.9 each respectively.
(a) Estimate whether the average price for 100 mL of Steven Chicken Soup for each packaging is more than $2. Explain briefly.
(b) Based on the result of (a) , which packaging of Steven Chicken Soup is more economical?
15. (a) Round off 2 558 to the nearest hundred.
(b) How many significant figures does the approximate value obtained in (a) have?
1.7
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2009 Chung Tai Educational Press. All rights reserved.

16. (a) Round off 4.079 to 2 decimal places.
(b) How many significant figures does the approximate value obtained in (a) have?
17.
Complete the following.
(a) 554

(corr. to 2 sig. fig.)
(b) 6 742 .
1

(corr. to 1 sig. fig.)
(c) 0 .
398 5

(corr. to 3 sig. fig.)
(d) 0 .
016 9

(corr. to 2 sig. fig.)
18.
Complete the following.
(a) 87 460

87 000 (corr. to sig. fig.)
(b) 2 .
543

2 .
5 (corr. to sig. fig.)
(c) 1 .
88

2 (corr. to sig. fig.)
(d) 0 .
014 87

0 .
014 9 (corr. to sig. fig.)
19.
Round off the following values to (i) 4 significant figures, (ii) 3 significant figures.
(a) 300.156
(b) 94 098
(c) 0.670
67
(d) 4.000
51
20.
Some chemical substances measure 1.899
8 g in weight by Victor. Round off the weight of the chemical substances to
(a) 2 significant figures.
(b) 3 significant figures.
(c) 4 significant figures.
1.8
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2009 Chung Tai Educational Press. All rights reserved.

21.
There are $20 802.08 in Joanna’s savings account. To give each of the following approximate values, how many significant figures should the amount in the savings account be rounded off to?
(a) $20 802
(b) $20 800
(c) $20 000
22.
Find the values of the following expressions, correct to 3 significant figures.
(a) 14 .
32

32 .
84
(b) 0 .
049

10 .
92

0 .
067

5 .
093
(c)
(d)
23 .
34

11 .
1
8 .
5

9 .
4
13
23.
Carmen bought three items from a shopping centre for $132.8, $145.9 and $78.5. How much should she pay? (Give your answer correct to 3 significant figures.)
24.
Joe completed a 1 000 m race in 3 minutes 10 seconds. Find his average speed in m/s, correct to
2 significant figures.
25. (a) Round off 6.947 to 3 significant figures, then round off the result to 2 significant figures. Write down the approximate value obtained.
(b) Round off 6.947 to 2 significant figures directly. Write down the approximate value obtained.
(c) Are the approximate values obtained in (a) and (b) the same?
26. (a) Consider the expression
4
11

1
3
. To give the approximate value 0.03, how many significant figures should the result of the expression be rounded off to?
1.9
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2009 Chung Tai Educational Press. All rights reserved.

(b) Consider the expression
4
(
11

1
3
)

1 000 . To give the approximate value 30, how many significant figures should the result of the expression be rounded off to?
(c) Are the results of (a) and (b) the same?
27.
A number is rounded off to give an approximate value 1 200. To give this approximate value, how many significant figures may the number be rounded off to? Illustrate your answer with examples.
1.10
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2009 Chung Tai Educational Press. All rights reserved.