MODULE 3: SCIENTIFIC NOTATION and SQUARE ROOTS

E-Module: Reconfiguring to the New Normal Mathematics

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After going through with this module, you are expected to learn and apply the key

concepts of Scientific Notation and Square Roots, which are essential in constructing

real-life situations specifically to:

1. Determine the significant digits of a given number.

2. Express numbers in scientific notation and in standard form 3. Determine the principal square root of a number

4. Solve for the dimensions of a plane figure applying the concept of square roots

5. Create a furniture design showing the Area and dimension of a plane figure.

which will help you become future Furniture Designer.

MODULE 3: SCIENTIFIC NOTATION and

Timeframe: SQUARE ROOTS

205 MINUTES

Hi! I am your

Furniture

Designer!


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A. SCIENTIFIC NOTATION Did it ever occur in your mind how far the distance of the moon is from the earth? Or the distance of the sun from the earth?

If you notice the distance is a large number, in so doing you need to have a strategy in order to compare and to compute the given number. But, before that you need to determine first the significant digits that you will need to use in order to be able to express the number in scientific notation.

SIGNIFICANT DIGITS

Rules for determining Significant Digits

Rule 1: All nonzero digits are significant ➢ 5.219 (4 significant digits) ➢ 26, 175 (5 significant digits)

Rule 2: Final zeros or trailing zeros to the right of the decimal point are significant.

➢ 5.0 (2 significant digits) ➢ 8.900 (4 significant digits)

Rule 3: Zeros found between two significant digits are significant. ➢ 1.0078 (5 significant digits) ➢ 35.0012 (6 significant digits) ➢ 106 007 045 (9 significant digits)

Rule 4: Leading zeros or zeros as placeholders are not significant. ➢ 0.0004 (1 significant digit) ➢ 23 000 (2 significant digits)

What are the Rules to determine the Significant Digits?


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Now, that you have an idea on how significant digits are determine, it is now time for you to find out how to express the scientific notation of a given number.

Steps in Converting to Scientific Notation

Step 1: Put the decimal after the first significant digit,

Step 2: Indicate how many places the decimal moved by the power of 10.

🖙 If the movement is to the left, the exponent is positive.

300, 000, 000 = 3 × 108

🖙 If the movements is to the right, the exponent is negative.

0.000 000 8 = 8 × 10−7

A number is expressed in scientific notation if it is in the form 𝑵 × 𝟏𝟎𝒎 when 𝟏 ≤ 𝑵 < 𝟏𝟎 and m is the

exponent and must be an integer. Note: m can be positive or negative.

How do we

express a number

in scientific

notation?

Measurements of physical quantities can vary from very

small to very large. Such numbers are kind of tedious to

write, difficult to read, and hard to compute. Thus, you

can write these numbers in a form that makes them easier

to work with. Specifically, you use the power of 10 to

rewrite each number.

Scientific Notation is a concise way of expressing a very

large or very small numbers

Convert to Standard Notation

Move the decimal point according to the exponent.

3.75 × 108

Positive exponent, move to the right.

3.75000000

Negative exponent, move to the left.

0.0007

= 375 000 000 = 0. 000 7


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B. PRINCIPAL SQUARE ROOTS OF A NUMBER Now that you have learned to multiply signed numbers, you might want to consider products in

which the same number is repeated as a factor. But your focus will be on the principal square root of a number.

First that you will do is, to define and then determine the principal square root of a given number. Complete the graphic organizer.

What is the relationship between squaring a number and finding the square root?

Key Concept

Read the problem below.

The square base of the Great Pyramid of Giza covers

almost 562, 000 square decimeters. How could you

determine the length of each side of the base?

I think the word means…

How does this word fit with the other words and

Square

root

concepts I know?

Are there parts of the word that I recognized?

What makes this an important word for me to know?

The square root is a number which produces a specified quantity when multiplied by itself. "7 is a square root of 49"

It also means one of its two equal factors.

Numbers such as 1, 4, 9, 16, and 25 are called perfect squares because they are squares of integers.


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5 2

A. Find each square root.

1)

√64 2) ±√1.21

√64 = 8 Find the positive square root of 64; 82 = 64

±√1.21 = ±1.1 Find both square roots of 1.21; 1.12 = 1.21

3) 25 −√ 36

25 5 −√ = −

36 6

4) √−16 There is no real square root because no number times itself is equal to -16.

Find the negative square

root of 25 36

; ( ) = 25

6 36

B. Finding Square Roots by Inspection Example 1:

32 = 3 x 3 = 9 9 is called the square of 3 (second power of 3), written as 32 = 9

Example 2:

3 is called a square root of 9, written as √9 = 3

122 = 12 x 12 = 144 144 is called the square of 12 (second power of 12), written as 122 = 144

Example 3:

12 is called a square root of 144, written as √144 = 12

√4 = 2, because 22 = 4 √1 = 1, because 12 = 1

√0 = 0, because 02 = 0 √25 = 5, because 52 = 25

In the given examples, you have found the square root of number greater than or equal to zero. Square roots of nonnegative numbers are always real numbers. On the other hand, square roots of negative numbers are not real numbers. They are called imaginary numbers.

C. Finding Square Roots Using Trial and Error

Supposed you were asked to find√196. You know√100 = 10, because 102= 100. Therefore, √196 > 10


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Try 12: 122 = 144. Therefore 12 is too small. Try 13; 132 = 169. Therefore, 13 is too small. Try 14; 142 = 196. Therefore √196 = 14 This is what we mean by finding the square root by trial and error.


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D. Finding the Square Root using the Long Division

Algorithm 1) √1296 Steps:

1) Separate your number’s digits into pairs starting from the right. √𝟏𝟐 ′𝟗𝟔 This method uses a process similar to long division to find an exact square root digit-by-digit.

2) Start with the first group, which is 12. Find the largest integer whose square is less than

or equal to the first pair. Here, you can say 3. When you multiply 3 x 3 = 9, and 9 < 12. Can we use 4? If you multiply 4 x 4 = 16, which 16 > 12.

3) Subtract the number you just calculated form the first pair. As with long division, the next step is to subtract the square you just found from the first pair you

just analyzed. Write this number underneath, same as you do with division

4) Drop down the next pair. In this case, it is 96. - Move the next pair in the number whose square root you're solving for down next to the

subtracted value you just found. Next multiply the number in the top right quadrant by two (this is a constant number in this process) and write it in the bottom right quadrant. Next to the number you just wrote down, set aside space for a multiplication problem you'll do in the next step by writing '"_×_="'.

5) Fill in the blank spaces in the right quadrant. - You must fill each blank space you've just written in the right quadrant with the same

integer. This integer must be the largest integer that allows the result of the multiplication problem in the right quadrant to be lower than or equal to the current number on the left.

6) Subtract the number you just calculated from the current number on the left. - Continue with the long-division style chain of subtraction. Take the result of the multiplication

problem in the right quadrant and subtract it from the current number on the left, writing your

answer below.

7) Repeat Step 4 until you get zero. In this case of the example, you need to stop since you already got zero.

Therefore√1296 = 36


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Solve the following Word problems.

1) FURNITURE The top of a folding table is a square whose area is 289 square inches. What is the side length of the tabletop?

Solution:

You need to identify the shape of the tabletop and then use the formula in finding the side length. In this case you will use A =s2

A = S2

289 = S2

√289 = √𝑆2 17 = S

Answer: The side length of the tabletop is 17 inches.

2) SQUARE GARDEN A mother of two decided to make a square garden of organic green leafy vegetables. She planned on doing it at the back of her house. Her available plot has an area of 6.25 square meters. She also decided to place fence around it. How many meters should the dimension of her fence will be?

Solution:

A = S2

6.25 = S2

√6.25 = √𝑆2 2.5= S

Answer: Each side will have a dimension of 2.5 meters


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PE 4.1. THE SCIENTIFIC NOTATION

Name: Section and Batch No:

Teacher: Ricardo S. Paig, EdD. Subject: Math 7

Date: Score:

A. Write the following in Scientific Notation

B.

The examples given after every lesson may not be enough for you to have a deeper understanding on the lessons discussed. At this point of the module, engage yourselves with activities that would enhance more of what you have understood in the lesson. You can answer the activities here in the module wherein a work zone is provided. Furthermore, you will also answer worksheets uploaded in the PSDE-desk or in your Google Classroom. Aside from the uploaded worksheets, you will also be engaging in games and other activities synchronously. The activities will be rated accordingly.

1) 246 =

2) 0.008503 =

3) 10 408 =

4) 5 690 =

5) 20 045 =

6) 0.103 =

7) 2043.009 =

Write the following in Standard Form.

8) 𝟑 × 𝟏𝟎−𝟒 =

9) 𝟐. 𝟏𝟓 × 𝟏𝟎𝟔 =

10) 𝟑. 𝟎𝟓 × 𝟏𝟎𝟓 =

11) 𝟐. 𝟒𝟗𝟓 × 𝟏𝟎−𝟔 =

12) 𝟓. 𝟏𝟐𝟑 × 𝟏𝟎−𝟏 =

13) 𝟏. 𝟓 × 𝟏𝟎−𝟓 =

14) 𝟑. 𝟎𝟔 × 𝟏𝟎𝟕 =

15) 𝟓. 𝟏 × 𝟏𝟎−𝟑 =

Work Zone


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Work Zone PE 4.2. SQUARE ROOTS

Name: Section and Batch No:

Teacher: Ricardo S. Paig, EdD Subject: Math 7 Date:

Score:

Extract the square root of the following numbers. Show your

solutions.

1) √625 2) √5929

3) √8281 4) √13225

5) √1764


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In order to reinforce the skills and concepts of this module, you are task to answer the activities found on your textbook, Math Connections in the Digital Age 7. Worksheets will also be uploaded in our LMS.

Check the table below for the list of exercises in your textbook that you are going to answer and the directions.

Directions: Read each instruction carefully. Write your answers on a whole bond paper and upload it to your LMS account, which you will submit on or before the indicated date of submission.

Reinforcement

Exercises Topic Page No. Item No.

Date of Submission

RE 4

Scientific Notation

Pages 78 -

79

Chapter Review Set III and IV

To be given during the synchronous

schedule.

During the synchronous session, you will be given game activities which would reinforced your learning.

In this part of the module, you will be tasked to answer the Word Problem in the class work of your Google Classroom during your synchronous session.

1) The area of the square

plant box is 16 square

units. Find the perimeter

of the figure.


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PRODUCT OF LEARNING

Section: Batch No. Name Grade 7- Score:

Teacher: Ricardo S. Paig, EdD Date:

Directions: Create your own furniture applying the concepts of Square Roots.

Rubric for the Futuristic Furniture!

Total Score: ______________ The dead line is set at the end of the synchronous meeting of module 4.

PL 4: Futuristic Furniture

In this part of the e-module, you will create your own recipe applying the concepts learned in Rational numbers, which will be graded according to the rubrics. Additional instruction will begiven during your synchronous session. In preparation, you should have the following materials:

1) Bond paper or colored paper 2) Colored Pens or Pencils 3) Ruler, Paste or glue, Pair of scissors

GOAL Your task is to create your own furniture showing the dimensions of the length and width and its area.

ROLE Furniture Designer

AUDIENCE Designers

SITUATION A furniture shop owner announced that they are going to have a contest showcasing different new concepts of furniture that they would add to their 2022 collection and the theme would be futuristic furniture.

PRODUCT A creative design of the furniture

STANDARDS FOR ASSESSMENT

You will be graded based on the rubric designed suitable for your task and performance.

Areas 5 4 3 2 1

Content Addresses the topic

completely Addresses the

topic very

satisfactorily

Addresses the

topic

satisfactorily

Addresses the

topic fairly

Addresses the

topic poorly

Presentation Creative and neat

in all aspects

Creative and

neat in most

aspects

Creative and

neat in few

aspects

Manifests a

little evidence

of creativeness

and neatness

Not creative

nor neat

Promptness Submit on or

before the deadline 1 day late 2 days late 3 days late 4-5 days late

Note: The product of Learning will be submitted through the classwork in your Google Classroom.

Your Performance Task:


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1) Textbook: Math Connections in the Digital Age, By: Janice F. Antonio; Ryan Bruce; Luis Allan Melosantos; Susan Robles and Josephine Sacluti,

2) 21st Century Mathematics A Vision for A Better Future, By: Ma. Luisa V. Villano, et Al

3) Grade 7 Mathematics: Patterns and Practicalities; G;adys C. Nivera, PhD 4) Soaring 21st Century Mathematics 7: Simon L. Chua, DT, Josephine L. Sy Tan; Srvir D. Ubarro;

Archieval A. Rodriguez, EdD; Jonathan C. Glorial, Manuel T. Kotah 5) McGraw–Hill OURMATH Grade 7

Philippine K to 12 Curriculum 6) Website Linksas Referencesandfor Learning Activities

www.kahoot.it www.google.com Google Classroom PSD E-desk Splashlearn.com https://www.wikihow.com/Calculate-a-Square-Root-by-Hand https://www.google.com.qa/url?sa=i&url=http%3A%2F%2Fwww.clipartpanda.com %2Fclipart_images%2Fsquare-foot-gardening- 64706459&psig=AOvVaw31XWK39x4jOqDvZBN2xaME&ust=1603564384087000&so urce=images&cd=vfe&ved=0CA0QjhxqFwoTCNilkYuty-wCFQAAAAAdAAAAABAO

References:

http://www.kahoot.it/

http://www.google.com/

https://www.wikihow.com/Calculate-a-Square-Root-by-Hand

http://www.google.com.qa/url?sa=i&url=http%3A%2F%2Fwww.clipartpanda.com

MODULE 3: SCIENTIFIC NOTATION and SQUARE ROOTS

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