General Physics 1

Quarter 1 - Module 1 Units, Physical Quantities and

Measurements

Senior High School

General Physics 1- Grade 12

Alternative Delivery Mode Quarter 1 - Module 1: Units, Physical Quantities and Measurements

First Edition, 2020

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General Physics 1

Quarter 1 - Module 1:

Units, Physical Quantities and Measurements

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Senior High School

Table of Contents

What This Module is About i

What I Need to Know i

How to Learn from this Module ii

Icons of this Module ii

What I Know iii

First Quarter

Lesson 1: Unit Conversion and Scientific Notation

What I Need to Know 1

What‟s In: Check It Out! 2

What‟s New: Pass the Message 3 What Is It: Learning Concept: Scientific Notation 4

Significant Figures 5

What‟s More: Exercises 6

What Is It: Learning Concepts: Unit Conversion 7-9

What‟s More: Exercises 10

What I Have Learned: 11

What I Can Do: Performance Task and Enrichment Activity 12

Sample Format for the Performance task……………………13-14

Lesson 2: Accuracy and Precision

What‟s In 15 What I Need to Know 15

What‟s New 16

What Is It: Learning Concepts: Accuracy & Precision 17-18

What‟s More: Data Analysis 19

What I Have Learned: 20

Assessment: (Post-Test) 21

Key to Answers 22

Appendices A &B 23

References 24

Module 1

Units, Physical Quantities and

Measurements

What This Module is About

This module demonstrates your understanding and skill in solving measurement

problems involving conversion of units as well as expressing it in scientific notation. Since Physics and measurement are inseparable, measurement entails accuracy and precision. This module emphasizes the difference of the two; accuracy and precision and illustrates its equal importance in taking measurement.

This module will help you explore the basic concepts on topics that will help you

solve measurement problems in the succeeding topics in Physics.

This module has two (2) lessons:

● Lesson 1- Unit Conversion and Scientific Notation

● Lesson 2- Accuracy and Precision

What I Need to Know

After going through this module, you are expected to:

1. Solve measurement problems involving conversion of units, expression of measurements in scientific notation (STEM_G-12EU-Ia-1) 2. Differentiate accuracy from precision (STEM_G-12EU-Ia-2)

How to Learn from this Module

To achieve the learning competencies cited above, you are to do the following:

• Take your time reading the lessons carefully.

• Follow the directions and/or instructions in the activities and exercises diligently.

• Answer all the given tests and exercises.

Icons of this Module

What I Need to This part contains learning objectives that

Know are set for you to learn as you go along the

module.

What I know This is an assessment as to your level of

knowledge to the subject matter at hand,

meant specifically to gauge prior related

knowledge

What‟s In This part connects previous lesson with that

of the current one.

What‟s New An introduction of the new lesson through

various activities, before it will be presented

to you

What is It These are discussions of the activities as a

way to deepen your discovery and under-

standing of the concept.

What‟s More These are follow-up activities that are in-

tended for you to practice further in order to

master the competencies.

What I Have Activities designed to process what you

Learned have learned from the lesson

What I can do These are tasks that are designed to show-

case your skills and knowledge gained, and

applied into real-life concerns and situations.

What I Know

MULTIPLE CHOICE:

Directions: Read and understand each item and choose the letter of the correct answer. Write

your answers on a separate sheet of paper.

1. Which of the following is equivalent to half a meter? A. B. C. D.

2. A book has a mass of , how many kilograms does it weigh?

A. B. C. D.

3. Which of the following has the smallest value?

A. B. C. D. 4. The average thickness of the leg of an ant is . How many millimeters is this?

A. B. C. D.

5. Which of the following relationships of quantities is TRUE? A. C. B. D.

6. Which of the following is the BEST example of a number expressed in scientific notation?

A. C. B. D.

7. What is written in standard form? A. B. C. D.

8. The speed of light in a vacuum is about . Which of the following values in scientific notation is its equivalent?

A. C. B. D.

9. MOR radio station in Cagayan de Oro city operates at a frequency of 91.9 Mega Hertz.

What is written in standard form? A. C. B. D.

10. Which of the following is equal to ? A. B. C. D.

Lesson

1

Unit Conversion and Scientific Notation

What I Need to Know

Physics is an experimental science. Thus, experiments are performed in order to test

hypotheses. How do we make conclusions? Conclusions in experiment are derived from measurements. Experiments are performed to measure physical quantities. Physical quantities can be expressed in terms of a number of fundamental quantities. Mass, distance, time are some of these fundamental quantities. A physical quantity will only make sense if compared to a reference standard. For example, a cloth you bought from Everbest Store means that the cloth‟s length is times a meter stick (or a tape measure that is 1-m long). Here, the meter stick is considered as our reference standard. Therefore, stating that the cloth is 3.5 is not as informative.

Look at the figure to the right. How difficult will it be without a standard?

To make sure that scientist throughout the world means the same thing when referring to a measurement; standards have been defined for measurements of time, mass and length.

In this lesson, you are to solve measurement problems involving conversion of units, expression of measurements in scientific notation.

What’s In You have learned in your Grade 11 Chemistry the rules of significant figures. Recall that when we say significant figures these are the digits in a number that indicates reliability of a measurement.

Check It Out! Determine the number of significant figures of the values given below:

1. 0.0025 ___________

2. 12. 00030 ___________

3. 3.1416 ___________

4. 20.20 ___________

5. 0. 4 ___________

Rules in Determining the Number of Significant Figure: (A short recall)

1. All nonzero digits are significant.

2. All zeros between nonzero digits are significant.

3. All zeros before the first nonzero digit are NOT significant.

4. All zeros to the right of the last nonzero digit are significant.

This concept which you learned in your previous science subject will be used in our entire topic involving measurement. Thus, it is important to remember and apply these rules.

What’s New

PASS THE MESSAGE

A. Situation:

You received a text message from your service provider as shown in the screen of your cellular phone.

You need to send the message below but the

message is too long to send as one text message. Shorten this to create the shortest text message possible.

“Hi Kayla! Today, I got drenched in the rain while

walking home from school since I forgot to bring my umbrella. I can‟t believe it! My bag wasn‟t zipped all the way. When I got home all my papers got soaked. I cannot read our homework to be passed tomorrow. Kindly send it to me. Thank you so much!”

Write you message in the space provide in the screen of your cellular phone below.

“You are nearing the end of your payment period and you only have one text message left before you go over

the limit!”

_______________________________

_______________________________

_______________________________

_______________________________

_______________________________

_______________________________

_______________________________

What Is It

If we shorten a message, we should do it in a way that the message will be useful and easy to understand. Physical quantities vary from very large numbers (e.g. the speed of light in a vacuum = ) to very small numbers (length of a certain wavelength of visible light of ). For scientists and students like you writing large or very small numbers in its standard form can be a waste of time, energy and even your resources like ink and paper.

Scientific Notation Scientific notation also called exponential notation is a convenient way of writing values using the power of ten notation wherein we can determine the number of significant digits as well as the place value of the digit. Place values are denoted by prefixes. (See appendix A for the SI prefixes found in the last page of this lesson) Format: where: - the characteristic digit, may be any digit from 0-9

– the mantissa digits, may be any digit from 0-9 – base

– exponent, the number of times the decimal point is moved to either towards left or right

Rules in expressing standard notation to scientific notation:

1. When the decimal point is moved from right to left, the result is positive exponent.

Example: = =

2. When the decimal point is moved left to right, the result is negative exponent.

Example: Rules converting scientific notation back to standard notation are shown below.

1. Move the current decimal point according to the number of places based on the exponent (+) positive exponent – move to the RIGHT Example:

( ) negative exponent – move to the LEFT Example:

Rules in Addition and Subtraction involving scientific notation

1. When two or more quantities are added or subtracted, make sure the exponents are the same. [ ]

2. Add/subtract the number. Keep the exponent the same.

Example:

(a)

(b) -Since exponents are not the same, choose one to adjust. -LARS- (here we will adjust to have an

exponent of )

-From , we will move two decimal places to the left since we added

two to the exponent, that becomes

Rules in Multiplication and Division involving scientific notation

1. Powers of ten are added in multiplication

Example:

2. Powers of ten are subtracted in division

Example:

(

)

Significant Figures

1. In adding or subtracting quantities, the least number of decimal places in any of the numbers being added or subtracted should also be the number of the decimal places in the answer.

Example:

+ (one decimal place) LEAST

2. In multiplying or dividing quantities, the least number of significant figures in the input

number should also be the number of significant figures in the answer. Example:

x

(two decimal places)

(four decimal places)

(ONE decimal place)

(four significant figures)

(three significant figures) (LEAST)

(three significant figures)

What’s More

Exercises: Write you answer on a separate sheet of paper.

1. Apply the rules in identifying the number of significant figures in each of the following: (a) 0. 00054 (d) 0. 016500 (b) 830 (e) 32.0040

(c) 356, 000 (f)

2. Express the following numbers in scientific notation: (Answers should include three significant figures)

(a) 65, 000 (c) 2, 450, 000 (b) 0. 001327 (d) 0. 00001997

3. Perform the indicated operations: (All answers should be expressed in scientific notation.

Apply the rules for significant figures in your final answer.)

(a)

(b) (

(c) ( )

(d)

(e)

4. Convert the given standard notation below to scientific notation. Then, perform the indicated operation. Apply the rules for significant figures in your final answer.

What Is It

Unit Consistency and Conversion of Units

There are two major systems of units in the world namely; SI (derived from French

Syteme International) units also known as Metric system and the English system. Although the system of units used by engineers and scientists is the metric system since 1960, some countries continue to use the English system of units like for example the United States of America. However, the conversions between the SI unit and English system of units have been well-defined. (See appendix B found in the last page of this lesson for conversion factors) Multiplying and/or dividing units just like ordinary algebraic expressions give an easy way to convert a quantity from one unit to another to be dimensionally consistent. Example:

(a) To convert to

Conversion factor to be used:

(b) To convert in meters per second

Conversion factors to be used:

(c) To convert

to

Conversion factors to be used:

[

]

(d) Converting units with different prefixes (See appendix A for the SI prefixes found in the last page of this lesson)

(i.) Example: convert 5 Megameter to meter

(ii.) Example: convert to

=

(iii.) Example: to

kilo means so,

* ANOTHER way to do this: to Step 1: subtract exponents

*kilo has exponent of and centi has exponent of

3 subtract -2 = 5 from kilo to centi

Step 2: move decimal places according to difference of exponents to the direction of wanted unit.

* move the decimal 5 places to the right (toward centi)

or

5 decimal places to the right

(iv.) Example: to

milli means so, =

conversion factor (See appendix A for the SI prefixes found in the last page of this lesson)

* ANOTHER way to do this: to

Step 1: subtract exponents

*milli has exponent of and deci has exponent of

-1 -3 = 2 deci milli

Step 2: move decimal places according to difference of exponents to the direction of wanted unit.

* move the decimal 2 places to the left (toward deci)

2 decimal places to the left

What’s More

Exercises: Write you answer on a separate sheet of paper.

1. Below are the given measurements. Convert it as indicated. (a) into

(b) into

(c) into

(d) into

(e) into (f) to

(g) to

2. Indicate which is greater (>) or lesser (<) by writing the correct symbol. If the quantities are equal write (=). Show your solution.

(a)

(b)

(c)

(d)

What I Have Learned

I. General Instruction: Solve the following measurement problems involving

conversion of units. Write your answer which is in standard notation into scientific notation and apply the rules in significant figures in expressing it into scientific notation. Write your answer on a separate sheet of paper including your solution.

1. Joeff, who is an exchange student from Germany, is studying in the United States. He wishes to buy a new pair of jeans, but the sizes are all in inches. If his waist size is

, what is its waist size in ?

2. The total area of the alveoli in the human lung is about .What is the area in

(a)

(b)

3. A Chevrolet Camaro convertible travels along the highway at a speed of . What is it the speed of the car (a) in ? (b) in ?

4. The Spirochetes, contain very thin bacteria with some species having cell diameters of

about .What is its diameter in ?

5. A government owned land will be set converted as a new wildlife refuge. Its dimensions

are by . Find the area of the land in .

II. Check your understanding!

1. Explain the importance of having a standard in measurement.

2. What‟s the advantage(s) of writing quantities in scientific notation?

What I Can Do

Performance Task: Measurement

Objectives:

Use appropriate measuring tool to take the measurement of physical quantities such as height and weight.

Convert the values to its equivalent units. Apply the rules of significant figures.

Measure the height and mass of your family member using appropriate measuring tool.

Gather the data and write it on the space provided for the data and results.

Take its equivalent height in cm and ft using conversion factor.

Take also its equivalent mass in grams and pounds.

Refer to the format provided in the next page.

Provide pictures on this task you performed.

Enrichment Activity: Practice exercises!

Refer to Appendix A for the SI prefixes found in the last page of this lesson. Fill-in the blanks with the correct values to justify the relationship of the quantities given. Write your answer on a separate sheet of paper.

6.

7.

8. 100 L = ________ mL

9.

10.

Name: ______________________________ Date Performed: ______________________

Performance Task #1: Measurement

Objective(s): Data and Results:

Name of your family members

HEIGHT *Measuring instrument used: _________________ ___________

MASS *Measuring instrument used: ___________________________________

Solution: (This is for the conversion of units)

Documentation: (Pictures)

Lesson

2

Accuracy and Precision

What’s In

In lesson 1, you have learned how to express very large and small physical quantities into scientific notation applying the number of significant figures. You also learned solving measurement problems involving conversion of units.

In this next topic, you will learn the definition of two important terms when we talk about measurements; accuracy and precision as well as its importance. You will also familiarize measuring instruments of varying precision and its advantage.

What I Need to Know

Often times, accuracy and precision are used interchangeably. However, these two

terms mean different things. As what you have learned in the previous topic, physicists perform experiments and these experiments involve measurements. It is important to be both accurate and precise in taking scientific measurements.

Why do you think it is important to be both accurate and precise in measurement? Can

you think of situations encountered in daily life that need to be accurate and precise? What do you think will happen if measurements are in accurate and less precise?

In this lesson, you are to differentiate accuracy from precision.

What’s New

General Instruction: Write your answer on a separate sheet of paper.

I. Study the image below. The bull‟s-eye represents the accepted true value. Each cross represents a repeated measurement of the same quantity. Describe each of the figures by choosing its description inside the box.

II. What is your basis for your choices in describing the figures above? What is your idea about accuracy? How about precision?

Precise and Accurate C. Not accurate but precise

Accurate but not precise D. Not accurate and not precise

Figure 1 Figure 2

Figure 3 Figure 4

What Is It

Accuracy and precision in measurements are important in many aspects of the world; may it be in the field of research, medicine, electronics/technology, manufacturing, and among others. Take for example, inaccurate dose of medicine may harm patient. In the same way, inaccurate measurements used in appliances for example may cause it to explode, even might spark fire that will cause harm to humans and properties. Even a difference of 0.01 might lead to undesirable results.

Accuracy refers to the closeness of the measurement to the true value or accepted

value. On the other hand, precision refers to the closeness among several measurements that have been obtained in the same way. Let us differentiate accuracy and precision in the context of a basketball player making a basket. We can say that a basketball player has a high degree of accuracy if the player always makes a basket even though he strikes in different positions of the rim. However, if he does not make many baskets but always strikes in the same position of the rim, then he has high degree of precision but not accurate. This concept is also the same with the figures shown in the previous activity showing targets on a dart board.

To better understand accuracy and precision of measurements, consider the example

below. Example: You, a student as part of your activity, weigh the new golf ball five times or five trials. The results are as follows: , , , , . The accepted value

for the mass of a new golf ball is . Observe that the average of the five values from five trials is close to the accepted value. Therefore, we can say that the measurement has high accuracy. If we consider the individual measurements, observed that they agree among the five measurements. Therefore, we can say that the measurements are precise. To ensure high accuracy and precision, one consideration is using appropriate measuring instruments designed to fit the purpose. Just take for example; if you want to measure a piece of wood, tape measure is suitable. But if you are going to use a tape measure in measuring smaller objects, do you think it will yield an accurate and precise measurement? Do you expect an accurate and precise measurement if you will use a ruler in measuring the eternal diameter of a thin wire? Let us familiarize three measuring instruments (as shown below), its advantages and its precision.

A ruler can measure longer/larger objects. The smallest scale division is or .

A vernier caliper allows to measure length including outside dimensions, inside dimensions and depth of smaller objects with more precision and accuracy. It can measure up to or decimal place in which makes it good to use in small and precise

measurements.

Micrometer is used to make accurate measurements of the thickness of a sheet of paper and the external diameter of thin wires. It can measure up to or decimal place in.

Study the picture of scale A and scale B on the right. Which scale is more accurate?

Why do you say so?

What’s More: Data Analysis

General Instruction: Analyze the measurement data set provided and describe the date set

in terms of accuracy and precision. Coin diameter A gold coin has an „accepted‟ diameter of 28.054 mm. Two students are asked to measure the diameter of four gold coins. Student A uses a simple plastic ruler. Student B uses a precision measuring tool called a micrometer.

Student A – plastic ruler Student B – micrometer

27.9 mm 28.0 mm 27.8 mm 28.1 mm

28.246 mm 28.244 mm 28.246 mm 28.248 mm

1. Calculate the average value for each set of measurements

Student A – plastic ruler Student B – micrometer

2. Compare the average value for each set with the accepted value:

● Which student‟s data is more accurate? Justify your answer. ● Which student‟s data is more precise? Justify your answer.

3. Explain any odd findings:

(Adopted from http://sciencelearn.org.z)

What I Have Learned

Check your understanding! Answer the following questions. Write you explanation on a separate sheet of paper.

1. Is there a difference in the accuracy of measurements of the reading if the units

used vary?

Why?

2. Up to what precise measure could each instrument be read?

3. Which of these three measuring devices:ruler, verner caliper and micrometer is the most versatile? Justify your answer.

4. The smallest unit on a ruler is 1mm. Two students measured the width of a wooden block and recorded them as 5.25 cm and 5.27 cm. Analyze the data gathered. Are these two equally precise? Comment.

5. Can measurements be accurate but not precise? Justify your answer by citing a

specific example.

6. Two students, John and Jay are given a small cylinder of aluminium of known

mass and asked to determine its density. (The „accepted‟ density of aluminium is 2.702 g/cm3.) Since density is mass/volume, the students need to calculate the volume of the cylinder. The height and diameter of the cylinder need to be measured in order to calculate its volume John is told to use a simple plastic ruler and to make four independent measurements for each dimension. Jay is told to use a precision measuring tool called a micrometer.

John – plastic ruler Jay – micrometer

2.2 g/cm3 2.3 g/cm3 2.7 g/cm3 2.4 g/cm3

2.703 g/cm3 2.701 g/cm3 2.705 g/cm3 5.811 g/cm3

a. Which student‟s data is more accurate? Cite factor(s) that might affect the

measurement‟s accuracy.

b. Which student‟s data is more precise? Cite factor(s) that might affect the measurement‟s precision.

Assessment: (Post-Test)

Direction: Select the letter of your choice. Write it in CAPITAL form. Your answers should be written on a separate sheet of paper.

1. What is the sum of , , and ? Apply rules in significant figures.

A. C. B. D.

2. You are using an electronic stop watch in one of your experiments in Physics. The digital

reading displays along with accuracy to how may second? A. C.

B. D.

3. The density of aluminium is

. An experiment in the laboratory was performed to

measure the density of the material. The data in the choices below came from the four groups who performed. Which of the following measurements is most accurate?

A.

C.

B.

D.

4. The diameter of a certain virus is as viewed under a microscope. How

would this be expressed in scientific notation?

A. C.

B. D.

5. Rio de Grande river has a total length of . What is this length in ?

A. C.

B. D.

6. A foreigner is driving his car along North Luzon Express way (NLEX) at a speed of

. Can he be charged off over speeding considering the maximum speed along this express way is .

A. Yes, because is beyond the maximum speed of . B. No, because is less than the maximum speed of C. No, because is jus equal to the maximum speed of D. Not enough data is given to determine if he is over speeding or not.

7. Which of the following sets of measurements are precise?

A. 1.50 mm, 1.72 mm, 1. 09 mm, 1. 84 mm B. 0.9 cm, 0.95 cm, 0.80 cm, 0.63 cm C. 1.20 m, 1.02 m, 0.97 m, 1. 42 m D. 0.84 dm, 0.85, 0.82, 0.83

8. Which of the following relationships of quantities is NOT true?

A. C. B. g D.

9. Which of the following values is equivalent to ?

A. C. B. D.

10. What is 7.5 millimeters expressed in centimeters?

A. B. C. D.

Assessment: Key to Answers

A. Pre-test

1. B 2. C 3. C 4. D 5. A 6. B 7. C 8. C 9. B 10. C

B. Post test

1. A 2. A 3. B 4. C 5. C 6. B 7. D 8. C 9. A 10. C

APPENDICES APPENDIX A. Prefixes Used with SI Units

APPENDIX B. Conversion Factor

Length

Mass

References

Manuals/Modules

Department of Education Central Office. Most Essential Learning Competencies

( MELCs). 2020.

Websites:

2020. Nebula2.Deanza.Edu. http://nebula2.deanza.edu/~lanasheridan/4A/Rulers-VernierCalipers-Mircometers.pdf.

2020. 4.Files.Edl.Io. https://4.files.edl.io/cc9f/08/26/18/225914-021efdd7-e111-4f98-

8564-5388f1bf7d14.pdf.

2020. Mlbgsd.K12.Pa.Us. https://www.mlbgsd.k12.pa.us/cms/lib/PA09000085/Centricity/Domain/83/lab_-

_accuracy_and_precision.pdf.

"Measurement, Accuracy And Precision Of Data | Grant Instruments". 2020. Grant Instruments. https://www.grantinstruments.com/measurement-accuracy-and-

precision-of-data.

"Multiple Choice Questions Answers - Online Quiz Tests". 2020. Mcqslearn.Com.

https://www.mcqslearn.com/.

"New Page 1". 2020. Pstcc.Edu.

http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/

Experiment%2001web.htm.

"Precision And Accuracy". 2020. Science Learning Hub.

https://www.sciencelearn.org.nz/resources/1880-precision-and-accuracy.

"Science Learning Hub". 2020. Science Learning Hub. http://sciencelearn.org.nz.

"Science Learning Hub". 2020. Science Learning Hub. http://sciencelearn.org.nz.

"Using The Vernier Calipers & Micrometer Screw Gauge | Department Of Physics". 2020. Phy.Uct.Ac.Za. http://www.phy.uct.ac.za/courses/phylab1/vernier.