SENIOR
HIGH SCHOOL
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General Physics1
Quarter 1 – Module 1:
Title: Measurements
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Science – Grade 12
Alternative Delivery Mode
Quarter 1 – Module 1: Measurements
First Edition, 2020
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General Physics1
Quarter 1 – Module 1:
Measurements
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Introductory Message
For the facilitator:
Welcome to the General Physics 1 12 Alternative Delivery Mode (ADM) Module on
Measurements!
This module was collaboratively designed, developed and reviewed by educators
both from public and private institutions to assist you, the teacher or facilitator in
helping the learners meet the standards set by the K to 12 Curriculum while
overcoming their personal, social, and economic constraints in schooling.
This learning resource hopes to engage the learners into guided and independent
learning activities at their own pace and time. Furthermore, this also aims to help
learners acquire the needed 21st century skills while taking into consideration
their needs and circumstances.
In addition to the material in the main text, you will also see this box in the body of
the module:
Notes to the Teacher
This contains helpful tips or strategies
that will help you in guiding the learners.
As a facilitator you are expected to orient the learners on how to use this module.
You also need to keep track of the learners' progress while allowing them to
manage their own learning. Furthermore, you are expected to encourage and assist
the learners as they do the tasks included in the module.
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For the learner:
Welcome to the General Physics 1 12 Alternative Delivery Mode (ADM) Module on
Measurements!
The hand is one of the most symbolized part of the human body. It is often used to
depict skill, action and purpose. Through our hands we may learn, create and
accomplish. Hence, the hand in this learning resource signifies that you as a
learner is capable and empowered to successfully achieve the relevant
competencies and skills at your own pace and time. Your academic success lies in
your own hands!
This module was designed to provide you with fun and meaningful opportunities
for guided and independent learning at your own pace and time. You will be
enabled to process the contents of the learning resource while being an active
learner.
This module has the following parts and corresponding icons:
What I Need to Know
This will give you an idea of the skills or
competencies you are expected to learn in
the module.
What I Know
This part includes an activity that aims to
check what you already know about the
lesson to take. If you get all the answers
correct (100%), you may decide to skip this
module.
What’s In
This is a brief drill or review to help you link
the current lesson with the previous one.
What’s New
In this portion, the new lesson will be
introduced to you in various ways such as a
story, a song, a poem, a problem opener, an
activity or a situation.
What is It
This section provides a brief discussion of
the lesson. This aims to help you discover
and understand new concepts and skills.
What’s More
This comprises activities for independent
practice to solidify your understanding and
skills of the topic. You may check the
answers to the exercises using the Answer
Key at the end of the module.
What I Have Learned
This
includes
questions
or
blank
sentence/paragraph to be filled in to
process what you learned from the lesson.
What I Can Do
This section provides an activity which will
help you transfer your new knowledge or
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skill into real life situations or concerns.
Assessment
This is a task which aims to evaluate your
level of mastery in achieving the learning
competency.
Additional Activities
In this portion, another activity will be given
to you to enrich your knowledge or skill of
the lesson learned. This also tends retention
of learned concepts.
Answer Key
This contains answers to all activities in the
module.
At the end of this module you will also find:
References
This is a list of all sources used in
developing this module.
The following are some reminders in using this module:
1. Use the module with care. Do not put unnecessary mark/s on any part of
the module. Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer What I Know before moving on to the other activities
included in the module.
3. Read the instruction carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your
answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not
hesitate to consult your teacher or facilitator. Always bear in mind that you are
not alone.
We hope that through this material, you will experience meaningful learning
and gain deep understanding of the relevant competencies. You can do it!
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What I Need to Know
This module was designed and written with you in mind. It is here to help you
master the measurements. The scope of this module permits it to be used in many
different learning situations. The language used recognizes the diverse vocabulary
level of students. The lessons are arranged to follow the standard sequence of the
course. But the order in which you read them can be changed to correspond with
the textbook you are now using.
The module has one lesson, namely:

Lesson 1 – Least Concept to Estimate Error
After going through this module, you are expected to:
1. Use the least count concept to estimate errors associated with single
measurements.
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What I Know
Choose the letter of the best answer. Write the chosen letter on a separate sheet of
paper.
Choose the letter of the best answer. Write the chosen letter on a separate sheet of
paper.
1. Considering the correct number of significant figures, evaluate the
following operation, 3.73 x 5.7 = _____.
a. 21
c. 21.26
b. 21.00
d. 21.261
2. Compute 3.24 m + 0.532 m to the correct number of significant
figures.
a. 3.77
c. 3.8
b. 3.772
d. 4.00
3. The sum of 1.04 + 2.1135 + 3.1 + 3.403 is_____
a. 9.6565
c. 9.66
b. 9.6
d. 9.70
4. Solve: 7.45 x 108 + 4.97 x 10-2 – 6.67 x 105 is equal to___
a. 7443.33 x 105
c. 7.44333 x 10-2
b. 7.44 x 108
d. 7443.330000497
5. Which of the following examples illustrates a number that is correctly
rounded to three significant figures?
a. 0.03954 g to 4.040 g
c. 20.0332 g to 20.0 g
b. 4.05438 g to 4.054 g
d. 103.692 g to 103.7 g
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6. Which of the following numbers contains the designated CORRECT
number of significant figures?
a. 0.00302
2 significant figures
b. 0.04300
5 significant figures
c. 1.04
2 significant figures
d. 3.0560
4 significant figures
e. 156 000
3 significant figures
7. A calculator answer of 423.6059 must be rounded off to three
significant figures. What answer is reported?
a. 420
b. 423
c. 423.6
d. 423.7
e. 424
8. Which of the following is CORRECT?
a. 2.450 x 107 rounded to two significant digits 2.4 x 107
b. 3.56 rounded to two significant digits is 3.6
c. 77.889 x 106 rounded to three significant digits is 77.8 x 106
d. 122.5 rounded to two significant digits is 120
9. The following observations have been made: 64.52, 3.0, 11.081. the
correctly written sum is
a. 78.6
b. 78.60
c. 78.6010
d. 79
10.
The quantity 0.245 x 36.74 / 200.0 = 0.045007, computed from
measured values, should be written in an engineering report as
a. 0.04500
c. 4.50 x 10-2
b. 4.5 x 10-2
d. 5 x 10-2
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11. The mass of a watch glass was measured four times. The masses
were 99.997 g, 100.008 g, 100.001 g, 100.005 g. What is the average
mass of the watch glass?
a. 100.00 g
c. 100.005 g
b. 100.01 g
d. 100.00525 g
12. When performing the calculation 34.530 g + 12.1 g + 1 222.34 g, the
final answer must have
13.
a. only one decimal place
c. three significant figures
b. three decimal places
d. unit of g3
How many significant figures are in the measurement of 102 400
meters?
a. three
b. four
c. five
d. six
14. 923 g is divided by 20 312 cm3
a. 0.045 g/cm3
c. 0.0454 g/cm3
b. 4.00 x 10-2 g/cm3
d. 0.04 g/cm3
15. Complete the following problem: A piece of stone has a mass of
24.595 grams and a volume of 5.34 cm3. What is the density of the stone?
(remember that density = m/v)
a. 0.22 cm3/g
b. 4.606 g/cm3
c. 4.61 g/cm3
d. 0.217 cm3/g
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Lesson
1
Measurement
It is important to be honest when reporting a measurement, so that it does not
appear to be more accurate than the equipment used to make the measurement
allows. We can achieve this by controlling the number of digits, or significant
figures, used to report the measurement.
Measurement values are only as accurate as the measurement equipment used to
collect them. For example, measuring meters with a meter stick is rather accurate;
measuring millimeters (1/1,000 of a meter) with a meter stick is inaccurate. Using
significant figures helps prevent the reporting of measured values that the
measurement equipment is not capable of determining. A significant figure is
comprised of the fewest digits capable of expressing a measured value without
losing accuracy. As the sensitivity of the measurement equipment increases, so
does the number of significant figures. Knowing the rules for working with
significant figures can help your students. “Rounding” numbers is the usual
method of achieving significant figures. Once the appropriate number of significant
figures for any measurement, calculation, or equation is determined, students can
practice rounding their answers appropriately.
What’s In
Compare and contrast accuracy and precision; random and systematic error.
Notes to the Teacher
It is significant that learners had background on the use of
integers, decimal, exponent, mathematical operations.
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What’s New
To determine the number of significant figures in a number
use the following 3 rules:
1. Non-zero digits are always significant
2. Any zeros between two significant digits are significant
3. A final zero or trailing zeros in the decimal portion ONLY are significant
Example: .500 or .632000 the zeros are significant
.006 or .000968 the zeros are NOT significant
For addition and subtraction use the following rules:
1. Count the number of significant figures in the decimal portion ONLY of each
number in the problem
2. Add or subtract in the normal fashion
3. Your final answer may have no more significant figures to the right of the
decimal than the LEAST number of significant figures in any number in the
problem.
For multiplication and division use the following rule:
1. The LEAST number of significant figures in any number of the problem
determines the number of significant figures in the answer. (You are now
looking at the entire number, not just the decimal portion)
*This means you have to be able to recognize significant figures in order to use
this rule*
Example: 5.26 has 3 significant figures
6.1 has 2 significant figures
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What is It
Rules for Significant Figure
1. All non-zero numbers ARE significant. The number 33.2 has THREE
significant figures because all of the digits present are non-zero.
2. Zeros between two non-zero digits ARE significant. 2051 has FOUR
significant figures. The zero is between a 2 and a 5.
3. Leading zeros are NOT significant. They're nothing more than "place holders."
The number 0.54 has only TWO significant figures. 0.0032 also has TWO
significant figures. All of the zeros are leading.
4. Trailing zeros to the right of the decimal ARE significant. There are FOUR
significant figures in 92.00.
92.00 is different from 92: a scientist who measures 92.00 milliliters knows his
value to the nearest 1/100th milliliter; meanwhile his colleague who measured 92
milliliters only knows his value to the nearest 1 milliliter. It's important to
understand that "zero" does not mean "nothing." Zero denotes actual information,
just like any other number. You cannot tag on zeros that aren't certain to belong
there.
5. Trailing
zeros
in
a
whole
number
with
the
decimal
shown
ARE
significant. Placing a decimal at the end of a number is usually not done. By
convention, however, this decimal indicates a significant zero. For example, "540."
indicates that the trailing zero IS significant; there are THREE significant figures in
this value.
6. Trailing zeros in a whole number with no decimal shown are NOT
significant. Writing just "540" indicates that the zero is NOT significant, and there
are only TWO significant figures in this value.
7. Exact numbers have an INFINITE number of significant figures. This rule
applies to numbers that are definitions. For example, 1 meter = 1.00 meters =
1.0000 meters = 1.0000000000000000000 meters, etc.
So now back to the example posed in the Rounding Tutorial: Round 1000.3 to four
significant figures. 1000.3 has five significant figures (the zeros are between nonzero digits 1 and 3, so by rule 2 above, they are significant.) We need to drop the
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final 3, and since 3 < 5, we leave the last zero alone. so 1000. is our foursignificant-figure answer. (from rules 5 and 6, we see that in order for the trailing
zeros to "count" as significant, they must be followed by a decimal. Writing just
"1000" would give us only one significant figure.)
8. For a number in scientific notation: N x 10x, all digits comprising N ARE
significant by the first 6 rules; "10" and "x" are NOT significant. 5.02 x 104 has
THREE significant figures: "5.02." "10 and "4" are not significant.
Rule 8 provides the opportunity to change the number of significant figures in a
value by manipulating its form. For example, let's try writing 1100 with THREE
significant figures. By rule 6, 1100 has TWO significant figures; its two trailing
zeros are not significant. If we add a decimal to the end, we have 1100., with FOUR
significant figures (by rule 5.) But by writing it in scientific notation: 1.10 x 103, we
create a THREE-significant-figure value.
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What’s More
A. How many significant figures are in each of the
following numbers?
1. 1.234
2. 1.2340
3. 1.234 x 10-3
4. 1.2340 x 10-3
5. 1234
6. 12340
7. 0.012340
8. 12.34
9. 123.4
10. 1.23400 x 10-5
B. Express the following number in scientific notation
with correct significant figure.
1. 900 000 (3SF)
2. 3400 (2SF)
3. 45 (3SF)
4. 0.815 (2SF)
5. 0.00891 (2SF)
6. 4 500 (2SF)
7. 0.00766 (1SF)
8. 56 000 (2SF)
9. 34 000 (3SF)
10.8930 (4SF)
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What I Have Learned
1. Significant figures of a measured or calculated quantity are the meaningful digits
in it.
2. Any digit that is not zero is significant.
3. Zeros between non-zeros digits are significant.
4. Zeros to the left of the first non-zero digit are not significant.
5. For numbers with decimal points, zeros to the right of a non-zero digit are
significant.
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What I Can Do
What are the significant things do you have in your possession?
Who are the significant people surrounds you?
Cite rules to consider significant people and things that you have.
Assessment
Multiple Choice. Choose the letter of the best answer. Write the chosen letter on a
separate sheet of paper.
1.
Considering the correct number of significant figures, evaluate the
following operation, 3.73 x 5.7 = _____.
a. 21
c. 21.26
b. 21.00
d. 21.261
2. Compute 3.24 m + 0.532 m to the correct number of significant figures.
a. 3.77
c. 3.8
b. 3.772
d. 4.00
3. The sum of 1.04 + 2.1135 + 3.1 + 3.403 is_____
a. 9.6565
c. 9.66
b. 9.6
d. 9.70
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4. Solve: 7.45 x 108 + 4.97 x 10-2 – 6.67 x 105 is equal to___
a. 7443.33 x 105
c. 7.44333 x 10-2
b. 7.44 x 108
d. 7443.330000497
5. Which of the following examples illustrates a number that is correctly
rounded to three significant figures?
6.
a. 0.03954 g to 4.040 g
c. 20.0332 g to 20.0 g
b. 4.05438 g to 4.054 g
d. 103.692 g to 103.7 g
Which of the following numbers contains the designated CORRECT
number of significant figures?
a. 0.00302
2 significant figures
b. 0.04300
5 significant figures
c. 1.04
2 significant figures
d. 3.0560
4 significant figures
e. 156 000
3 significant figures
7. A calculator answer of 423.6059 must be rounded off to three significant
figures. What answer is reported?
a. 420
b. 423
c. 423.6
d. 423.7
e. 424
8. Which of the following is CORRECT?
a. 2.450 x 107 rounded to two significant digits 2.4 x 107
b. 3.56 rounded to two significant digits is 3.6
c. 77.889 x 106 rounded to three significant digits is 77.8 x 106
d. 122.5 rounded to two significant digits is 120
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9. The following observations have been made: 64.52, 3.0, 11.081. the
correctly written sum is
a. 78.6
b. 78.60
c. 78.6010
d. 79
10. The quantity 0.245 x 36.74 / 200.0 = 0.045007, computed from
measured values, should be written in an engineering report as
a. 0.04500
c. 4.50 x 10-2
b. 4.5 x 10-2
d. 5 x 10-2
11. The mass of a watch glass was measured four times. The masses
were 99.997 g, 100.008 g, 100.001 g, 100.005 g. What is the average
mass of the watch glass?
a. 100.00 g
c. 100.005 g
b. 100.01 g
d. 100.00525 g
12. When performing the calculation 34.530 g + 12.1 g + 1 222.34 g, the
final answer must have
13.
a. only one decimal place
c. three significant figures
b. three decimal places
d. unit of g3
How many significant figures are in the measurement of 102 400
meters?
a. three
b. four
c. five
14. 923 g is divided by 20 312 cm3
a. 0.045 g/cm3
c. 0.0454 g/cm3
b. 4.00 x 10-2 g/cm3
d. 0.04 g/cm3
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15. Complete the following problem: A piece of stone has a mass of
24.595 grams and a volume of 5.34 cm3. What is the density of the stone?
(remember that density = m/v)
a. 0.22 cm3/g
b. 4.606 g/cm3
c. 4.61 g/cm3
d. 0.217 cm3/g
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Additional Activities
The next station featured fifteen cards. Each card has a number that has
anywhere from one to five significant figures. Students didn't know this, but there
were three cards with one significant figure, three cards with two significant
figures, etc.
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Downloaded from
https://www.google.com.ph/search?source=univ&tbm=isch&q=picture+of+games+on+significant+figu
res&sa=X&ved=2ahUKEwifxYTk7avpAhUKA4gKHf--DDoQ420oCnoECAkQKg&biw=1366&bih=608
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What I Know
1. A
2. A
3. B
4. B
5. C
6. E
7. E
8. B
9. D
10. C
11. A
12. C
13. B
14. A
15. C
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What's More
A.
1. 4
2. 4
3. 4
4. 4
5. 4
6. 4
7. 4
8. 4
9. 4
10.4
B.
1. 900 x 103
2. 3.4 x 103
3. 450 x 101
4. 8.2 x 10-1
5. 8.9 x 10-3
6. 4.5 x 103
7. 8 x 10-3
8. 5.6 x 104
9. 3.40 x 104
10.8.930 x 103
Assessment
1. A
2. A
3. B
4. B
5. C
6. E
7. E
8. B
9. D
10. C
11. A
12. C
13. B
14. A
15. C
Answer Key
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References
Chhetri, Khadka Bahadur. Computation of Errors and their Analysis on Physics
Experiments. Tribhuvan University, Nepal.
Giancoli. Physics 215: Experiment 1 Measurement, Random Error, Error Analysis.
Sio, Janina Andrea et.al. Experiments: Errors, Uncertainties and Measurements
Laboratory Report. Manila, Philippines.
Tabujara Jr., Geronimo D.
K-12 Compliant Worktext for Senior High School
General Physics 1. Manila, Philippines: JFS Publishing Services
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For inquiries or feedback, please write or call:
Department of Education - Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex
Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
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