Chapter 1 Module

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 particularlevel 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 wholenumber may or may not be significant. Itdepends on how the estimation is made*All zeros after any non-zero digit in a wholenumber are not significant unless statedotherwise

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

4. For decimals less than 1, zeros preceding thefirst non-zero are not significant*All zeros before any non-zero digit in adecimal point are not significant

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

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


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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

Determine digit (x) to round off

Is it the number after xgreater or less than 5?

Add 1 to x

Is it extra digits after xlocated 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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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 inbrackets:

(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). .

(e)


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Find the value of each of the following and express each answer correct to the number of significantfigures 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 theaverage 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 theland, correct to 2 significant figures.

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

4. The length of a piece of rectangular card is 15.7 cm. its width is 12.4 cm. calculate the area, incm2, 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 thecylinder, correct to 2 significant figures. (Take = )


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6. The length, breadth and height of a rectangle are 7.5 cm, 12.5 cm and 10.5 cm respectively.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 totalmass, 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 = r3 and use = 3.142 ]

1.2 STANDARD FORMMATHEMATICS FORM 4

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1.2a State positive numbers in standard form

1. State the following in standard form

(a) 39 871(b) 0.006 73(c) 430 557(d) 0.000 523 6(e) 9 803 000(f) 0.00709

(g) 8833(h) 31 584(i) 680 000(j) 0.9233(k) 0.0463(l) 0.0005452

Solution:

2. Write the following numbers in standard form

(a) 72.5(b) 202.8(c) 6879(d) 325 000

(e) 0.00006(f) 0.008382(g) 0.0546(h) 0.6118

Solution:


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3. Express 5 630 000 in standard formA. 5.63 x 104

B. 5.63 x 106

C. 5.63 x 10-4

D. 5.63 x 10-6

1.2b State the numbers to standard form as single numbers

1. State the following as single numbers

(a) 5.872 x 106

(b) 3.012 x 10-2

(c) 2.015 89 x 104

(d) 4.305 x 10-3

Solution:

2. Express the following in single numbers

(a) 2.73 x 104

(b) 3.638 x 105

(c) 9.445 x 106

(d) 6.229 x 10-3

(e) 7.47 x 10-4

(f) 8.06 x 10-5

Solution:


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3. Write each number below in standard form or as single numbers

(a) 12(b) 189 200(c) 542.800(d) 54 670 000(e) 0.12(f) 0.0415

(g) 0.000 72(h) 0.000 001 23(i) 23 x 103

(j) 0.079 x 106

(k) 3900 x 10-4

(l) 0.001 21 x 106

Solution:


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1.2c Perform operations involving numbers in standard form

1. Solve the following and state your answer in standard form.

(a) 23 800 + 3947(b) 0.040 021 – 0.000 5461

(c) 3.21 x 105 – 7.593 x 104

(d) 2.01 x 10-4 + 3.75 x 105

Solution:

2. Evaluate the following, giving your answers in standard form

(a) 7.4 x 102 – 3.7 x 102

(b) 7.9 x 105 – 8.8 x 104

(c) 6.7 x 10-8 – 4.9 x 10-8

(d) 2 x 10-6 – 2.4 x 10-8

(e) 7.2 x 10-4 – 0.0000084

Solution:

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Chapter 1 Module