Approximation and Estimation

Question 1

round off each of the following numbers to the nearest 10
(a) 275
(b) 273.1

Answer 1

(a) 280
(b) 270

Question 2

correct 96.482 to
(a) 1 decimal place
(b) the nearest whole number

Answer 2

(a) 96.5
(b) 96

Question 4

what rule is this example: number 7258 has 4 significant figures

Answer 4

1) All non-zero digits are significant

Question 5

what rule is this example: number 302.008 has 6 significant figures

Answer 5

2) All zeros between non-zero digits are significant

Question 6

what rule is this example: number 0.057 has 2 significant figures

Answer 6

3) In a decimal, all zeros before a non-zero digit are not significant

Question 7

what rule is this example: number 0.0120 has 3 significant figures

Answer 7

4) In a decimal, all zeros after a non-zero digit are significant

Question 8

what rule is this example: number 7500 has 2 significant figures

Answer 8

5) The zeros at the end of a whole number may or may not be significant, depending on how the number is rounded off

Question 9

round 3748 to 3 significant figures

Answer 9

3750

Question 10

round 0.00470989 to 4 significant figures

Answer 10

0.004710

Question 11

round 4971 to 2 significant figures

Answer 11

5000

Question 12

round 0.09999 to 2 and 3 significant figures

Answer 12

0.10, 0.100

Question 13

round 8982 to 2 significant figures

Answer 13

9000

Question 14

round 0.0060195 to 4 significant figures

Answer 14

0.006020

Question 15

round 0.9999 to 3 significant figures

Answer 15

1.00

Question 16

area of a square is 131cm²

(i) find the length

(ii) find the perimeter

Answer 16

(i) √131 = 11.4cm (to 3 s.f.)
(ii) 11.446 cm x 4 = 44.8cm (to 3s.f.)

Question 17

Joyce used a calculator to evaluate 31.5 + 9.87 - 2.1 and obtained the answer 392.7.
Without doing the actual calculation, use estimation to check whether Joyces answer is reasonable.
Then use a calculator to evaluate 31.5 + 9.87 - 2.1. Is your estimated value close to the actual value?

Answer 17

31.5 + 9.87 - 2.1
≈ 32 + 10 - 2
= 40

Joyces answer, 392.7, is not reasonable.
Using a calculator, the actual answer is 39.27.
hence, the estimated value, 40, is close to the actual value of 39.27.

Question 18

A wallet costs 225 Thai baht. The conversion rate is 1 baht = S$0.041212.
Without using a calculator, estimate the price of the wallet in S$.

Answer 18

100 baht ≈ S$4
200 baht ≈ S$8
50 baht ≈ S$2
25 baht ≈ S$1
225 baht = 200 baht + 25 baht ≈ S$8 + S$1 = S$9
∴ price of wallet ≈ S$9

Question 19

Answer 19

Method 1:
Option A:
200 g costs about $6.
100 g costs about $3.
50 g costs about $1.50.
250 g = 200 g + 50 g costs about $6 + $1.50 = $7.50.
Option B:
250 g costs $7.45.
Does this mean that Option B gives the better value for money since $7.45 < $7.50?
In this case, we have overestimated the cost of 250 g of coffee powder in Option A (see Method 2).

Method 2:
Option A:
200 g costs $5.80 = $6.
100 g costs about $3.
50 g costs about $1.50.
250 g = 200 g + 50 g costs about $5.80 + $1.50 = $7.30.
Option B:
250 g costs $7.45.
∴ Option A gives the better value for money since $7.30 < $7.45.

Question 20

Answer 20

Method 1:
Option A:
200 g costs about $6.
100 g costs about $3.
50 g costs about $1.50.
250 g = 200 g + 50 g costs about $6 + $1.50 = $7.50.
Option B:
250 g costs $7.45.
Does this mean that Option B gives the better value for money since $7.45 < $7.50?
In this case, we have overestimated the cost of 250 g of coffee powder in Option A (see Method 2).

Method 2:
Option A:
200 g costs $5.80 = $6.
100 g costs about $3.
50 g costs about $1.50.
250 g = 200 g + 50 g costs about $5.80 + $1.50 = $7.30.
Option B:
250 g costs $7.45.
∴ Option A gives the better value for money since $7.30 < $7.45.

Question 21

Estimate the ratio of the area of the shaded region to that of the unshaded region in the figure
below.

Answer 21