SENIOR HIGH SCHOOL
General Physics1
Quarter 1 – Module 1:
Title: Measurements
Science – Grade 12
Alternative Delivery Mode
Quarter 1 – Module 1: Measurements
First Edition, 2020
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12
General Physics1
Quarter 1 – Module 1:
Measurements
Introductory Message
For the learner:
Welcome to the General Physics 1 12 Alternative Delivery Mode (ADM) Module.
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 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.
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. Read the instruction carefully before doing each task.
2. Observe honesty and integrity in doing the tasks.
3. Finish the task at hand before proceeding to the next.
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!
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.
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.
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
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 non-zero
digits 1 and 3, so by rule 2 above, they are significant.) We need to drop the final 3,
and since 3 < 5, we leave the last zero alone. so 1000. is our four-significant-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.
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.
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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