Chapter 1- Standard Form

SMK. KOTA KLIAS, BEAUFORT CHAPTER 1: STANDARD FORM 1.1 Significant Figures Rules to remember A. For whole numbers Rules a. 12344 i. All non zero digits are significant figures b. 3487923 a. 2008 ii. Zero between the digits is significant b. 160005 figures a. 2000 iii. Zero after the digit not significant figures b. 12300 B. For decimal numbers Rules i. Zero after the decimal point not significant a. 0.00011 figures b. 0.007858 ii. Zero after the digits are significant figures a. 2.300 b. 0.034000

Examples 5 significant figures 7 significant figures 4 significant figures 6 significant figures 1 significant figures 3 significant figures Examples 2 significant figures 4 significant figures 4 significant figures 5 significant figures

Rounding off Round off the following numbers correct to the number of significant figures indicated within the brackets. 64 349

(3)

6 4 3 4 9

4<5 digit to be rounded 3, is unchanged. Before the decimal point each digit is replaced by 0

64 300 ( 3 significant figures ) 0.064 34

(3)

0. 0 6 4 3 4

4<5 digit to be rounded 3, is unchanged. After the decimal point digit 4 is dropped.

0.0643 ( 3 significant figures )

SMKKK

707.2

(2)

7 0 7. 2

7>5 , 1 is added to the digit to be rounded 0, 0+1=1 .After decimal point, digit 2 is dropped.

710 ( 2 significant figures ) 7.072

(2)

7.0 7 2

7>5 , 1 is added to the digit 0, 0+1=1 After the decimal point, digits 7 and 2 are dropped.

7.1 ( 2 significant figures )

1

1. How many significant figures are there in the following numbers? a. 1245 = 4 sig. fig e. 71.001 i. 0.023 b. 220000 f. 1.230 j. 0.134 c. 1340 g. 35.43 k. 0.00230 d. 4004 h. 0.0003 l. 0.12300 2. Round off the following numbers correct to the number of significant figures given. 4 significant figures 3 significant figures 2 significant figures a. 2850 b. 0.003456 c. 23.670 d. 56782 e. 0.0006984 3. Calculate each of the following, Give your answer correct to the number of significant figures indicated in the brackets. a) 5.34 – 21.46 + 34.9 6.47 − 5.817 d) [3] 74000 [1]

b) 0.092 + 12.54 x 3.3 [2]

c) 4.361 ÷ 13.6 – 0.097 [4]

3.49 +6.58

e) 47 .6 −11 .96 [2]

f)

6 (0.378 −0.2961 ) 7

[2]

SMKKK

2

1.2 Standard Form General Form : A x 10 n 1 ≤ A < 10 and n is an integer 1. Write each of the following in standard form a) 327 b) 0.0007 3 2 7. = 3 x 10 2

c) 13200

.0 0 0 7 = 7 x 10 −4

d) 0.0012

e) 0.000006

f) 5503

g) 37890000

h) 0.000000000128

i) 78599

Calculator Check [ Casio fx 570MS ] 1. Change the mode of the calculator to Scientific Sci mode a) Press mode button 5 times or until you see “Sci” on the screen b) Choose the number under the “Sci” 2. The calculator will respond by displaying Sci 0 ∼ 9? (0 ∼ 9 refers to the number of significant figures) 3. Choose 3 for 3 significant figures ( 0.00 ×10 00 ) 4. Enter the following keys to write, example 327 in standard form 327= 5. The answer obtained from the calculator is 3.27 ×10 02 (Correct to 3 significant figures)

2. Convert the following numbers in standard form to single numbers

SMKKK

3

10 a) 1.3 ×

3

d) 9.35 ×10

−4

g) 4.115 ×10

5

−3

b) 2.13 ×10

4

c) 7.5 ×10

e) 3.45 ×10

6

f) 6.11 ×10

h) 5.005 ×10

−4

−6

i) 7.215 ×10 12

Calculator Check [ Casio fx 570MS ] 1. Change the mode of the calculator to Scientific Norm mode a) Press mode button 6 times or until you see “Norm” on the screen b) Choose the number under the “Norm” 2. The calculator will respond by displaying Norm 1 ∼ 2? 10 3 to single number 3. Enter the following keys to write, example 1.3 × 1 . 3 EXP 3 = you will obtain the answer 1300

3. Solve each of the following. Give your answer in standard form. a) 16 200 + 7600 b) 0.000702 – 0.000067 c) 345000 + 210000

SMKKK

4

d) 3.6 ×10

e) 3

+ 4.9 ×10

2

g) 4.2 ×10

6.6 ×10

f) 3

− 8.9 ×10

2

h) −3

+ 6.97 ×10

−4

3.1 ×10

5.16 ×10 5 + 4.5 ×10

4

i) −3

− 7.61 ×10

−4

8.25 ×10

−13

+ 9.5 ×10

4. Solve each of the following. Give your answers in standard form

SMKKK

5

−12

a)

b)

4.3 ×10

6

×6.9 ×10

6

× 2.14 ×10

10

d)

8.6 ×10

×9.25 ×10

15

÷8.5 ×10

−7

e)

6.8 ×10

g)

c) 11

2.31 ×10 5 4.67 ×10 20

SMKKK

2

−10

×9.56 ×10

f)

3.27 ×10

h)

2.57 ×10

6

1.7 ×10 16 5000

6.2 ×10

i)

−10

÷ 2.97 ×10 10

3.7 ×10 11 6.39 ×10 20

6

−6