Physical Quantities

1. Physical
Quantities and
Measurements
Week 1 Lesson 1

2. Learning Outcomes
The students will solve multi-concept, rich-content problems
involving measurement using experimental and theoretical
approaches.
INTENDED
LEARNING
OUTCOMES
MOST
ESSENTIAL
LEARNING
COMPETENCY
• Solve measurement problems involving conversion of
units, expression of measurements in scientific
notation
• Differentiate accuracy from precision
• Differentiate random errors from systematic errors
• Estimate errors from multiple measurements of a
physical quantity using variance

3. Table of Contents
Accuracy and
Precision
Percent of
Uncertainty
Measurement
Physical Quantity
Base Quantity
Derived Quantity
Conversion of Units
Significant Figures
Scientific Notations
Uncertainty
Types of Uncertainty
Estimating Uncertainties using
Variance
1
3 4
2

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6. Measuremen
t
0
1

7. Measurement
 A process of determining how large or
small a physical quantity is as compared to
a basic reference quantity of the same kind.
 The process of associating numbers with
physical quantities and phenomena.
 It is fundamental to the sciences; to
engineering, construction, and other
technical fields; and to almost all everyday
activities.

8. Physical
Quantity
Is a quantity that can be measured. It consists
of a numerical magnitude and a unit.
MAGNITUDE UNIT
It can be classified as Base Quantity and
Derived Quantity

9. Base Quantity
Is a quantity that cannot be expressed in terms
of other physical quantities.
In order to work with a consistent and coherent
measurement system, Système International
d’Unitès or SI Units is used.

10. Derived
Quantity
Are quantities obtained from a combination of
various base quantities and their units are
determined from the relation between the base
quantities and derived quantities.

11. Derived
Quantity
Are quantities obtained from a combination of
various base quantities and their units are
determined from the relation between the base
quantities and derived quantities.
Density =
𝑀𝑎𝑠𝑠
𝑉𝑜𝑙𝑢𝑚𝑒
=
𝑘𝑔
𝑚3

12. Prefixes
Are terms added before the units to indicate
smaller or larger values. This is to avoid writing
too many zeroes that may give rise to human
error.

13. Conversion of
Units
0
2

14. Conversion of Units
If the physical quantity is not in the SI unit, it
can be converted to SI unit using conversion
factor.

15. Conversion of Units
For Example,
How many minutes are there in 3 hours?
3 hrs 𝑥
60 𝑚𝑖𝑛𝑠
1 ℎ𝑟
= 180 mins
CONVERSION
FACTOR
GIVEN
UNIT
CONVERTED
UNIT

16. Scientific
Notation
Is a technique used to represent very small or large
numbers with a numerical representation in the form of:
N x 10n
Coefficient
whose value is
between 1-9
only
Power of 10

17. Scientific
Notation
For Example
How to express the following in the correct scientific notation?
a. 123456 m
b. 0.00123456 g
Steps:
1. Determine if the value is more or less than
1. If less than 1, its exponent is negative. If
it's more than 1, the exponent is positive.
2. If it is positive, move the decimal point to
the LEFT to until the coefficient becomes 1-
9 in value. If it is negative, move the
decimal point to the RIGHT.
3. Count the number of places you move the
decimal point. This number is the exponent.
123456 m = 1.23456 x 105 m
0.00123456 g = 1.23456 x 10-3 g

18. Scientific
Notation
For Example
How to express the following scientific notation into numbers?
a. 6.987 x 103 kg
b. 9.2938 x 10-5 m/s2
Steps:
1. If the exponent is positive,
move the decimal to the
RIGHT by the number of the
exponent. If the exponent is
negative, move to the LEFT
by the number of exponent.
6.987 X 103 kg = 6987 kg
9.2938 x 10-5 m/s2 = 0.000092938 m/s2

19. Operations on Scientific Notation
Addition and Subtraction
Step 1: Rewrite the numbers so that they all have the same power of ten by moving the
decimal place of coefficient with the smaller exponent.
Step 2: Add or subtract the numbers. Copy the power of ten.
Step 3: Rewrite the sentence in a scientific notation.
Example: 5.3×106+11.2×107
Multiplication and Division
Step 1: Multiply or Divide the coefficient
Step 2: For multiplication, add the exponents. For division, subtract the exponent.
Step 3: Rewrite the sentence in a scientific notation.
Example:
7 𝑥 105
2 𝑥 10−2 2.5 𝑥 109

20. Significant
Figures Is a method of reporting measured data or
values to present more accurate data.

21. Accuracy and
Precision
0
3

22. Accuracy and
Precision
Accuracy is how close a given set of measurements (observations or readings)
are to their true value, while precision is how close the measurements are to
each other.

23. Uncertainties
0
4

24. Uncertainty
These are measurements of physical quantities that tends to have mistakes or
errors from its true value due to various factors.
This can be caused by Systematic Errors or Random Errors
Systematic Error Random Error
Are due to the measuring device
being biased in some way so that
it reads consistently high or low. It
can be Instrumental, personal and
external errors
Are due to the experimental or
inherent difficulty in taking
accurate measurements

27. How Number of Uncertainties be
reported?
220 ± 5 cm
Value of the
quantity
Number of
uncertainty
Unit
This means,
220 cm + 5 = 225 cm
220 cm – 5 = 215 cm
Range of true value

28. How to get Percent of Uncertainty?
220 ± 5 cm
Solution,
±5
220
x 100 = 2.27%
Written as,
220 cm ± 2.27%

29. Sample
Problem
The correct value of the measurement is between 200ml and 230ml. Find the percent
uncertainty of the measurement and write the value correctly.
Step 1 Determine the correct value and the number of uncertainty
200𝑚𝑙+230𝑚𝑙
2
= 215 ml
215ml – 200ml = 15
230ml – 215ml = 15
Step 2 Calculate the Percent Uncertainty
±15
215𝑚𝑙
x 100 = 6.98%
Step 3 Write the correct value of the measurement
215 ml ± 6.98%

30. Estimating Uncertainties of Multiple
Measurement using Variance
Step 1 Take the MEAN of the values
Mean =
𝑥
𝑛
=
98.72
8
= 12.34
Step 2 Take the deviations of the values from the mean
Measurements (cm)
12.30
12.35
12.31
12.34
12.36
12.38
12.33
12.35
Measurements (x-mean) Deviation (d)
12.30-12.34 -0.04
12.35-12.34 +0.01
12.31-12.34 -0.03
12.34-12.34 0.00
12.36-12.34 +0.02
12.38-12.34 +0.04
12.33-12.34 -0.01
12.35-12.34 +0.01

31. Estimating Uncertainties using
Variance
Step 3 Get the Average Deviation (a.d.)
a.d. =
𝑑
𝑛
=
0.16
8
= 0.02
Step 4 Take the Average Deviations of the
Mean (A.D.)
Measurements (x-mean) Deviation (d)
12.30-12.34 -0.04
12.35-12.34 +0.01
12.31-12.34 -0.03
12.34-12.34 0.00
12.36-12.34 +0.02
12.38-12.34 +0.04
12.33-12.34 -0.01
12.35-12.34 +0.01
∑x = 98.72 ∑𝑑 = 0.16
Note: Summation of the deviation
without the regard of the sign.
A.D. =
𝑎.𝑑.
√𝑛
=
0.02
√8
= 0.01 cm
Step 5 Write the Numerical value of the Uncertainty
12.34 ± 0.01 cm
12.34
Mean (True Value) A.D. (Uncertainty)
0.01

32. Asynchronous Task

33. Asynchronous Task

34. Asynchronous Task

35. Asynchronous Task

36. Asynchronous Task

37. Performance Task:
Laboratory Activity

38. Rubrics
CRITERIA 1 2 3 4 5
Set-up and
Equipment Care
Set-up of equipment
is not accurate, help
is required with
several major details
Many necessary
supplies must be
found in mid-lab
Set-up of equipment
is generally workable
with several details
that need refinement
Some necessary
supplies must be
searched out
Set-up of equipment
is generally accurate
with 1 or 2small
details that need
refinement
All necessary
supplies on hand
All equipment
accurately placed
All necessary
supplies on hand
All equipment
accurately placed
All necessary
supplies onhand
Very neat and
organized
Following
Procedure
Lacks the
appropriate
knowledge of the lab
procedures Often
requires help from the
teacher to even
complete basic
procedures
Demonstrates
general knowledge of
lab procedures
Requires help from
teacher with some
steps in procedures
Demonstrates good
knowledge of the lab
procedures
Will ask peers for
help with problems in
lab procedures
Works to follow
each step before
moving on to the next
step
Demonstrates
sound knowledge of
lab procedures Will
discuss with peers to
solve problems in
procedures
Carefully follows
each step
Demonstrates very
good knowledge of
the lab procedures
Gladly helps other
students to follow
procedures
Thoroughly and
carefully follows each
step before moving
on to next step
Data Collection Measurements are
incomplete,
inaccurate and
imprecise
Observations are
incomplete or not
included
Symbols, units and
significant figures are
not included
Measurements are
somewhat inaccurate
and very imprecise
Observations are
incomplete or
recorded in a
confusing way
There are 3 or more
minor errors using
symbols, units and
significant digits or2
Measurements are
mostly accurate
Observations are
generally complete
Work is organized
Only 2 or 3 minor
errors using symbols,
units and significant
digits
Measurements are
accurate with
reasonable precision
Observations are
thorough
Work is generally
neat and organized
Includes symbols,
units and significant
digits
Measurements are
both accurate and
precise
Observations are
very thorough and
may recognize
possible errors in data
collection
Work is neat and
organized
Includes appropriate

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