Standard Form

CHAPTER 2
STANDARD FORM

- Pn. Sazazila Abdullah-

What will you learn?
2.1 SIGNIFICANT FIGURES
2.2 STANDARD FORM

Why do you learn this chapter ?

• In scientific field , very big or very small numbers are
commonly used . For example in astronomy , the
distance between two stars is usually millions of
kilometres while in the study of particles , the distance
between atoms is extremely small.

• Numbers written in standard form are widely used in the
field of science , engineering , astronomy and so on .

State the number of significant figures of the following

numbers . NUMBER OF SIGNIFICANT
FIGURES

1129 4

72.4 3

27.86 4

402 3

3006 4

20004 5

5107 4

300 1

50 1

• Example 2

• Round off the following measurements to the number of
significant figures indicated .

11 564 1 significant 2 significant 3 significant 4 significant
22 099 figure figure figure figure
30 783 10 000 12 000 11 600 11 560
198 232 20 000 22 000 22 100 22 100
0.0032181 30 000 31 000 30 800 30 780
198.73 200 000 200 000 198 000 198 200
4.0032 0.003 0.0032 0.00322 0.003218
0.12005 200 200 199 198.7
4 4.0 4.00 4.003
0.1 0.12 0.120 0.1201

Example 3
Round off each of the following numbers to the numbers of
significant figures stated in the brackets .
• a) 33.45 (1)
• = 30
• b) 20.08 (2)
• = 20
• c) 32.899 (3)
• = 32.9
• d) 70 016 (4) = 70 020

• Round off each of the following numbers to the numbers
of significant figures stated in the brackets .
e) 0.07 ( 2)
= 0.070
f) 0.0023(1)
= 0.002
g) 6.0085 (2)
=6.0
h) 23 016(1) = 20 000

• Round off each of the following numbers to the numbers
of significant figures stated in the brackets .
i) 572.15 (3)
= 572
j) 198 411 (3)
= 198 000
k) 167 000 (1)
= 200 000
l) 7.2345 (4)
= 7.235

• Round off each of the following numbers to the numbers
of significant figures stated in the brackets .
m) 850 900 (5)
= 850 900
n) 3.456 ( 2)
= 3.5
o) 51.754 (4)
= 51.75

• STANDARD FORM

A  10n ,

where 1  A  10, n is an int eger

Example 4

Write the following numbers in standard form

a) 23 000

= 2.3 104 ,

b) 5623

= 5.623 103,

c) 0.0042

= 4.2  103,

d) 0.01873

= 1.873 102 ,

Example 5

Express each of the following as a single number.

a) 8  105,

= 800 000

b) 9.3 106 ,

= 9 300 000

c) 3  102 ,

= 0.03

d) 2.7  104 ,

= 0.00027

Example 6

10• Fill in the blanks with the correct n

• a) 1 megajoule = 1 x 106 joule
• b) 1 miliampere = 1 x 103 ampere
• c) 1 kilowatt = 1 x 103 watt
• d) 1 nanogram = 1 x 109 gram

Example 7

• Calculate the values of the following and express your
answers in standard form .

• a) 3.4  104  6.1 104
 (3.4  6.1) 104
 9.5  104

• Calculate the values of the following and express your
answers in standard form .

• b) 9.3  105  2.13  104

 9.3101 104  2.13 104

 (0.93  2.13) 104

 3.06 104

• Calculate the values of the following and express your
answers in standard form .

• c) 1.8109
5 108

 0.36 1098

 0.36 1017

 3.6 101 1017

 3.6 1018

Thank you