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LESSON 1: MEASUREMENTS
Introduction
Physics is a body of facts giving an exact description of man’s experiences regarding the
physical world pertaining to matter, energy and their interactions not involving chemical
and biological changes
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Hence, it is a numerical description
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Learning Outcomes
After successful completion of this lesson, you should be able to:
Understand the concept of significant figures and how to handle them when
carrying out simple arithmetic operations
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Describe the three widely used systems of units
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Discussion
1
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Exact numbers are numbers with an infinite number of significant figures while
approximate numbers are numbers with limited number of significant figures
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1
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1

Rules for Counting Significant Figures
✓ Nonzero digits are always significant
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✓
Zeros to the left of nonzero digits (called leading zeros) are never
significant
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If a number contains a decimal point, the zeros to the right of it
are always significant
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00 has four significant figures
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The number 93,000 has at least two and at
most, five significant figures
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1
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2

1
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3

2005
10
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4
0
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0

Rules for Rounding Off
✓

If the digit you remove from the right-hand end of the number is 0, 1, 2, 3
or 4, then the last digit you keep is unchanged
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Significant Figures in Calculations
There are a few simple rules to follow in deciding how many significant figures to

keep
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That is, x = 3m has only one significant figure,
and expressing this value as x = 0
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If we instead wrote x = 3
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0030 km), we would imply that we know the value of x to two
significant figures
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Rule 2 — When multiplying or dividing, keep a number of significant figures in the
product or quotient no greater than the number of significant figures in
the least precise of the factors
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3

3
...
2

A bit of good judgment is occasionally necessary when applying this
rule:
9
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03 = 10
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8 technically has only two significant figures, it
is very close to being a number with three significant figures
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Rule 3 — In adding or subtracting, the least significant digit of the sum or
difference occupies the same relative position as the least significant
digit of the quantities being added or subtracted
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For example, suppose we wish to find the sum of three
numbers as follows:
103
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10
+ 0
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319 or 106
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By
rule 1, we should include only one doubtful digit; thus the result should
be expressed as 106
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*Note:

1
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Scientific Notation

Scientific Notation is a method of writing numbers in the following form:
n 10m, where n is any number between 1 and 10 (1 n 10) while m is any positive or
negative integer
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234 105
0
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010 10− 4
This method is used in expressing very large or very small numbers and in
indicating whether the zeros at the end of a number are significant or not
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0 103
5,000 = 5
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3

only the first zero is significant
all zeros are significant

Measurement of Physical Quantities

Physical quantity is a quantity, which actually exist and is therefore directly or
indirectly measurable in the laboratory
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A unit is a measure of a quantity that is equal to 1
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*Note: Units and standards can be defined freely
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Two kinds of physical quantities according to units:
✓

Fundamental quantities — quantities that are relatively easy to define and
choose a suitable standard
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In practice, the smallest possible number of fundamental quantities are chosen
and the rest of the other quantities are merely defined in terms of them
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4

Three Widely Used Systems of Units

1
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1

The International System of Units (SI)
SI System — abbreviation of the French equivalent of the English term
International System of Units
— metric system or the MKS system
— internationally accepted system of units
SI Fundamental Units
Quantity
time
length
mass
amount of substance
temperature
electric current
luminous intensity

Name

Symbol

second
meter
kilogram
mole
kelvin
ampere
candela

s
m
kg
mol
k
A
cd

7

✓

mass — resistance to force, which causes objects to move (the more
massive the object, the more force is needed to move the object
from rest)

✓

amount of substance — amount of material contained in an object in terms
of the number of atoms or molecules

✓

temperature — hotness or coldness of a substance

✓

electric current — amount of negative charges flowing

✓

luminous intensity — brightness of light

✓

MKS — stands for the first letters of the three base units of length (meter),
mass (kilogram), and time (seconds)

✓

standard of time in the SI system — second (s)
— the time required for a cesium – 133
atom to undergo 9,192,631,770
vibrations

Two advantages of the SI system:
1
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conveniently relates different units of measure using the SI prefixes added to
the unit
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4

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