This document discusses the importance of measurement in physics and introduces the International System of Units (SI Units) used to measure physical quantities. It provides definitions and examples of base units like the meter, kilogram, second, kelvin, and ampere. Prefixes are also introduced to write very large and small numbers in standard form with powers of ten. Examples are provided to convert between different units of length, mass, time, volume, velocity, pressure, and acceleration.

1. Introduction
Physics is an experimental science. Theories are
useful only if their predictions agree with the results of
experiments. So measurement plays an important
part in physics. Together with other scientists ,
physicists have agreed on a single system of units for
the measurement of physical quantities .
A physical quantity is clearly defined with a numerical
value and a unit. A physical quantity can be
measured using a standard size called the unit.
Units identify the quantity that has been measured.
The standard size used must
(i) be easily reproduced
(ii) not have its magnitude changed
(iii) be internationally accepted
Although various systems of units have been used
over the years, scientists have generally agreed to
use the International System of Units (S.I. Unit).
Units for the base quantities are known as base units,
i.e. metre , kilogram, second, Kelvin and
ampere.
The definition of base units.
The metre is the length of the path
traveled by light in vacuum during a time
interval of 1 of a second
299792458
The kilogram is the mass of a prototype
cylinder of platinum-iridium alloy that is kept
at the International Bureau of Weights and
Measures.
The second is 9192631770 periods of a
specified radiation from Cesium-133
atoms
The Kelvin is 1 of the
273.16
thermodynamic temperature of the triple point of
water
The ampere is the current carried by two long
parallel wires placed one meter apart, when the
attractive force per unit length between two
wires is 2 x 10-7
Nm-1
.
Prefixes
Prefix is a scientific notation word before the base
units and have certain value uses powers of 10.
Prefix Symbol Factor
Tera
Giga
Mega
Kilo
Desi
Centi
Mili
Mikro
Nano
Piko
T
G
M
k
d
c
m
µ
n
p
Standard Form
The radius of earth 6400000000 mm and the
diameter a metal wire is 0.00000045 km. What is the
best way to write these numbers ?
The best way is try to write the numbers in shorthand
form.
The shorthand form of writing numbers is called
standard form.
In general, the standard form number is
a x 10n
where 1 ≤ a<10
and n are positive integers or
negative integers.
6
LESSON 2
Units Of Measurement

2. Example 1
Write the following numbers in standard form.
(a) 0.00008 m (b) 5300 g
(c) 0.0068 cm (d) 567.13 km
(e) 345.2 x 104
m (f) 0.000078 x 10-6
s
(g) 7 x 10-5
x 8 x 106
(h) 3 x 108
+ 8 x 106
(i) 6.2 x 109
(j) 3.8 x 10-2
- 7.2 x 10-3
3.1 x 103
Solution
Example 2
Convert the following lengths into the units of metre.
(a) 2.3 km (b) 0.62 mm
(c) 3 x 106 cm
Solution
Example 3
Express 22.5 g in the units of
(a) kg (b) dg
Solution
Example 4
Express
(a) 73 kg in terms of mg
(b) 0.0045 ms in terms of Ms
Solution
Example 5
Convert
(a) 11.5 cm3 into the units of m3
(b) 72 km h-1 into the units of ms-1
(c) 5 g cm-3 into the units of kg m-3
Solution
7

3. 1 Which of the following is not true?
A The metre is the length of the path
traveled by light in vacuum during a time
interval of 1 of a second
299792458
B The kilogram is the mass of a prototype
cylinder of copper-aluminium alloy that is
kept at the International Bureau of
Weights and Measures.
C The second is 9192631770 periods of a
specified radiation from Cesium-133
atoms
D The kelvin is 1 of the
273.16
thermodynamic temperature of the triple
point of water
2 Every number can be written in ‘standard form’,
particularly in the cases of
A very small numbers
B very large numbers
C very small and very large numbers
3 The standard form for 15200 is
A 15.2 x 10 2
B 1.52 x 10 3
C 1.52 x 10 4
D 0.152 x 10 -4
E 1.52 x 10-5
4 The product of 2.4 x 10 -2
and 5.0 x 10 - 4
is
A 1.2 x 10 6
B 1.2 x 10 5
C 1.2 x 10- 5
D 1.2 x 10- 7
E 1.2 x 10 -8
5 If A = 2 x 10 - 4
and B = 3 x 10 - 5
then the value of A + 5B is
A 1.7 x 10 - 5
B 3.5 x 10 - 5
C 1.7 x 10 - 4
D 3.5 x 10 - 4
E 1.7 x 10 –3
6 What is 0.0455 kg expressed in standard form?
A 0.455 x 10 - 1 kg
B 4.55 x 10 - 2 kg
C 45.5 x 10 - 3 kg
D 455 x 10 - 4 kg
7 The prefixes according to their value in
ascending order are
A Giga,mega,kilo,centi
B Mikro,mili,centi,kilo
C Mega,giga,kilo,centi
D Centi,giga,mikro,mili
8 Radio 5 RTM station operates at 105 .6 M Hz.
The expression of the frequency in units of
Hz is
A 1.056 x 10 8 Hz
B 1.056 x 10 6 Hz
C 1.056 x 10 4 Hz
D 1.056 x 10 - 4 Hz
E 1.056 x 10 - 8 Hz
9 5 x 10 - 4 seconds is equivalent to
A 0.05 microseconds
B 0.5 microseconds
C 50 microseconds
D 500 microseconds
E 5000 microseconds
10 Which one of the following measurements is
different?
A 2.3 x 10 2 m
B 2.3 x 10 4 cm
C 2.3 x 10 6 mm
11 Which one of the following measurements is
smallest ?
A 1.5 x 10 2 kg
B 1.5 x 10 7 g
C 1.5 x 10 12 µ g
8
TUTORIAL 2

4. 12 The misprints of length according to their value
in ascending order are
A 7 x 10 - 4 km , 7 x 10 2 cm , 7 x 10 4 mm
B 7 x 10 2 cm , 7 x 10 4 mm , 7 x 10 - 4 km
C 7 x 10 4 mm , 7 x 10 - 4 km , 7 x 10 2 cm
13 The volume of a metal sphere is 12 cm 3.
This volume in units of m 3
is
A 1.2 x 10 - 2
B 1.2 x 10
- 3
C 1.2 x 10 - 5
D 1.2 x 10 – 7
E 1.2 x 10 - 9
14 The velocity of a car is 108 km h-1.
What is the velocity in units of ms-1
?
A 20 B 30
C 50 D 60
E 90
15 The pressure exerted by a box on a surface is
500 N cm – 2
. What is the pressure in units of
Pa? ( 1 Pa = 1 N m - 2
)
A 5 x 10 - 2
B 5 x10 -1
C 5 x 10 4
D 5 x 10 6
E 5 x 10 8
16 The acceleration of a trolley is 2000 cm s- 2
This acceleration in S.I. unit is
A 0.002 B 0.02
C 0.2 D 2
E 20
17 Which one of the following prefixes is less
then 1?
A Mega
B Desi
C Kilo
18 Which of the following is true?
A 0.00023 = 2.3 x 10 - 3
B 0.05 = 5 x 10 - 1
C 3450 = 3.450 x 10 4
D 46.531 =4.6531 x 10 4
E 5678.9 = 5.6789 x 10 3
19
Value of physical
quantities
S.I. unit
400 cm 2
m 2
216 km h -1
ms -1
4 mm 3 m3
1500 cm s -2
ms - 2
Complete the table above.
20
Readings
7.2 x 10 5
µm , 7.2 x 10-2
cm
7.2 x 103
mm and 7.2 x 10
- 6
km
The table above shows the measurement of
length for four different objects.
(a) Which reading is the longest ?
....................................................................
(b) Which reading is the shortest?
....................................................................
(c) Arrange the readings according
descending order.
....................................................................
....................................................................
(d) Which reading is more than 1 metre?
....................................................................
(e) A cube of sides 7.2 x 103
mm . State the
volume of the cube in unit of m3
9