1.1 Significant Figures

1.1 SIGNIFICANT FIGURESMATHEMATICS FORM 4

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1.1a Concept of significant figures

Significant figures: The relevant digit of an integer or decimal number rounded off to a value according to a particular level of accuracy

Properties used as a guide to round off a number to the required number of significant figures

Properties Examples

1. All non-zero digits are significant 42 (2 significant figures)62.29 (4 significant figures)

2. Zeros between non-zero digits are significant 2.08 (3 significant figures)2006 (4 significant figures)

3. Zero following a non-zero digit in a whole number may or may not be significant. It depends on how the estimation is made*All zeros after any non-zero digit in a whole number are not significant unless stated otherwise

20 (1 significant figures)200 (1 significant figures)2000 (2 significant figures)2000 (3 significant figures)

4. For decimals less than 1, zeros preceding the first non-zero are not significant*All zeros before any non-zero digit in a decimal point are not significant

0.8 (1 significant figures)0.08060 (4 significant figures)

5. Zeros following a non-zero digit after the decimal point are significant*All zeros after any non-zeros digit in a decimal are significant

3.60 (3 significant figures)26.00 (4 significant figures)


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PRACTICE

1. State the number of significant figures in each of the following numbers:

(a) 6050 (d) 0.600078

(b) 7.100 (e) 30.09

(c) 0.0280 (f) 80 004

2. State the number of significant figures in each of the following numbers:

(a) 876 (d) 0.0802

(b) 294.02 (e) 2.020

(c) 8.0 (f) 600

Determine digit (x) to round off

Is it the number after x greater or less than 5?

Add 1 to x

Is it extra digits after x located before or after decimal point?

Change the extra digits with zero

x does not change

Dropping the extra digits

NO

YES

AFTER

BEFORE


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1.1b Round off a positive number to a given number of significant figures

PRACTICE

1. Round off the following numbers to:(i) Correct to 3 significant figures(ii) Correct to 2 significant figures(iii) Correct to 1 significant figures

(a) 38 106 (d) 45.465 (g) 0.09707 (j) 59.593

(b) 4398.7 (e) 80.043 (h) 0.0002938 (k) 598.3

(c) 1998 (f) 0.03562 (i) 0.9997 (l) 0.003498


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2. Round off the following, correct to 3 significant figures.

(a) 6.229 (d) 8996 (g) 0.006497

(b) 99.45 (e) 0.8429 (h) 0.02096

(c) 709.3 (f) 0.06025

3. Round off each of the following numbers to the number of significant figures indicated in brackets:

(a) 78 534 (1) (b) 0.604 (2)

(c) 4768 (2) (d) 0.003745 (3)


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1.1c Operations involving a few numbers and significant figures

Find the value of each of the following, stating your answer correct to 2 significant figures.

(a) 7.5 + 0.48 ÷ 0.04

(b) 0.06 x 0.1 + 35.6 ÷ 50

(c) 6.84 ÷ 30 + 3.75

(d) 5.28 – 7.5 x 0.04

(e) (724 + 25.1) ÷ 0.2


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(f) 1.24 ÷ 0.4 + 0.8 x 4.2

(g) 0.06 x 0.4 + 0.084 ÷ 0.2

(h) 19.2 – 4.2 ÷ 0.5 + 9.1

(i) 0.21 + 4.1 x 5 – 6.5


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Find the value of each of the following, stating your answer correct to 3 significant figures.

(a) 9.658 x 3.2 + 6.248

(b) 1.254 ÷ 0.03 – 6.2549

(c) 85.22 x 0.0663 – 76.369

(d)15.6240.4

(e)85025x 32


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Find the value of each of the following and express each answer correct to the number of significant figures indicated in the brackets

(a) 0.028 ÷ 0.02 – 1.204 [3]

(b) 0.68 ÷ 0.2 – 0.296 [3]

(c) 0.3 x 0.04 + 1.074 ÷ 60 [2]

(d) 5.2 x 0.3 – 0.345 [3]

(e) 6.78 ÷ 10 x 3.1 [3]


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(f) 0.3(4 – 0.38) [2]

(g) 1.38 + 8.13 ÷ 0.3 [2]

(h) 58.72 – 24.13 x 2.2 [2]

(i) 0.6 x 0.8276 ÷ 0.12 [1]

(j) 36.7 + 10.6 x 0.3 [2]


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1.1d Solve problems involving significant figures

1. The height of the Petronas Twin Towers is about 451.9 m and each has 88 storeys. What is the average height of a storey? Give your answer, correct to 3 significant figures.

2. The width of a piece of land is 12.5 m and its length is twice its width. Calculate the area of the land, correct to 2 significant figures.

3. Mary borrows RM63 000 from a bank with an interest rate of 6.25% per annum. Calculate the interest she needs to pay after two years (simple interest). State your answer, correct to 3 significant figures.

4. The length of a piece of rectangular card is 15.7 cm. its width is 12.4 cm. calculate the area, in cm2, of this card, correct to 3 significant figures.

5. The volume of a cylinder is 54.5 cm3. The radius of the base is 3 cm. calculate the height of the

cylinder, correct to 2 significant figures. (Take π=227 )

6. The length, breadth and height of a rectangle are 7.5 cm, 12.5 cm and 10.5 cm respectively.


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Calculate the volume of rectangle, stating your answer correct to 4 significant figures.

7. A box contains 6 cans. Each can has a mass of 505 g. the box has a mass of 60 g. find the total mass, in g, of 6 cans and the box, stating your answer correct to 2 significant figures.

8. The diameter of a sphere is 8.45 cm. calculate its volume, in cm3, correct to 2 significant figures. [

Volume of sphere = 43πr3 and use π = 3.142 ]

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1.1 Significant Figures