1. The document discusses various concepts related to physical measurements including units, accuracy, precision, errors, and significant figures. 2. It explains different ways to express uncertainty in measurements using either estimated uncertainty with a ± sign or percentage uncertainty. Accuracy refers to how close a measurement is to the true value, while precision refers to the reproducibility of measurements. 3. The document outlines various units used in measurements like meters, kilograms, grams, seconds. It also discusses converting between different units using conversion factors.

1. CHAPTER 1:
PHYSICAL UNITS

2. 1.1 Measurement

3. Uncertainty in Measurement
 There are 2 way to express uncertainty:
 Estimated uncertainty is written with a ±
sign.
• If a ruler has precision of 0.1 cm, an
object has length of 8.8 cm is written as
8.8±0.1 cm.
 Percent uncertainty is the ratio of the
uncertainty to the measured value, multiplied
by 100:

4. Accuracy indicated how close a
measurement is to the accepted value.
It describes the nearness
measurement to the standard or true
value.
Accuracy

5.  Indicates how close together or how
repeatable the result are.
 Is the degree to which several
measurement provide answers that is
very close to each other.
 The lesser the scatter, it gives a
higher the precision.
Precision

6.  A measurement system can be accurate but
not precise, precise but not accurate, neither,
or both.

7. Figure 1 : Measuring the width of a board with a
centimeter ruler. The uncertainty is ± 1 mm.

8. Type of errors
Random Errors – are usually small and has
equal probability of being positive or
negative, example; parallax error (an
error due to incorrect eyes position
during the measurement), mistake in
measurement, wrong count etc.
Systematic Errors – Constant error due
to instruments, physical conditions of
the surrounding or physical limitation of
the observer.

9. Is an estimation of the difference between the
measured value and the real value. It also known as
error.
Example:
If the exact mass of an object is 5.0kg and you
estimated mass between 4.8kg and 5.2kg.
mass, m= 5.0kg
Absolute error, Δm= 0.2kg
Thus the mass, m= 5.0 ±0.2kg
Absolute error

10. Is the ratio of the absolute error to the
real/exact value of some measured
quantity.
Relative error

11. Example 1: If the exact mass of an object is 5.0kg
and you estimated mass between 4.8kg and 5.2kg.
Find the relative error and percentage error.
mass, m= 5.0kg
Absolute error, Δm= 0.2kg
Relative error = Δm= 0.2= 0.04
m 5.0

12. Example 2:
Find the percentage error of 3.16 ± 0.28 m.

14. The number of significant figures is the number
of reliably known digits in a number.
Significant figures

15. 1) All nonzero digits are significant:
i. 457 cm (3 S.F)
ii. 0.25 g (2 S.F)
2) Zero between nonzero digits are significant:
i. 1005 kg (4 S.F)
ii. 1.03 cm (3 S.F)
iii. 40500 (3 S.F)
3) Zero to left of the first nonzero digits in a
number are not significant:
1) 0.02 g (1 S.F)
2) 0.0026 cm (2 S.F)
4) When a number ends in zeros that are to the
right of the decimal point, they are significant:
1) 0.0200 (3 S.F)
2) 3.0 cm (2 S.F)

17. When two or more measured values are
added, subtracted, multiplying or dividing
the final calculated value must have the
same number of decimal places as that
measured value which has the least number
of decimal places.
Example:
X = 12.658cm + 2.35cm
= 15.01cm

18. • A physical quantity can be measured
using standard size called unit.
• For example: meter (m), kilogram
(kg), etc.
• This unit is called SI unit.
1.2 Units and standard of measurement
Units

19. • SI unit is an
International System of
Units that is accepted
by the Eleventh
Conference of Weights
and Measures in 1960. it
is used in science and
technology all over the
world.

20. • Anything that can be measured is
called physical quantities.
Measurement

21. Basic
Quantities
• It cannot be derived from any physical quantities
Basic quantities are the fundamental
physical quantities.

22. Derived
Quantities
• Derived quantities are constructed from a combination
of several basic quantities.
Quantities that can be obtained and
expressed in terms of basic quantities.
22

23. 23

24. Scientific Notation
A way of writing numbers that accommodates values
too large or small to be conveniently written in
standard decimal notation.
 In scientific notation, numbers are written in the
form,
An electron’s mass is about 0.000 000 000 000 000
000 000 000 000 000 910 938 22 kg.
In scientific notation, this is written
9.109822 x 10-31 kg.

26. 1.3 Unit Conversion
Conversion factor to remember :
 1 km = 1000 m
 1 m = 100 cm
 1 cm = 10 mm
 1 kg = 1000 g
 1 h = 60 min
 1 min = 60 s
 1 h = 3600 s

27. Since any quantity such as length can be measured
in several different units, it is also important to
know how to convert from one unit to another.
1 L = 1000 cm3
1m = 3.28 ft
1 yd = 3 ft
1ft = 12 in
1 in = 2.54 cm
1 mi = 1.61 km

28. Example:
1) 1µm = _________mm
2) 10µm2 = _________m2
3) 17Mm = _________m

29. Conversion of
Units
29

30. • 45 cm = ? km
30

32. Solution (i) :
kmx
km
x
m
km
cm
m
cmcm
5
1012
1000100
12
)
1000
1
)(
100
1
(1212





33. Solution (ii):

34. • 35 km.hr-1 = ? m.s-1
Example

35. • 20 kg.m-3 = ? g.cm-3
35