NUMBER SYSTEM ( LECTURE 5)

LESSON 5

Dear Students,

In the previous class we covered the following learning outcomes:

· summarize the decimal expansion of real numbers

· How to express the decimal expansion in the form p/q.

Let us go through the guidelines for  the  blog once again:

·         The text in Red, is to be written in your register

·         The text in blue is to be viewed by clicking on it

·         The text in green is to be practiced for home work

1.      take your SET-A Mathematics Register

2.      Our handwriting reflects a lot about us. It will be awesome if you use good presentation and cursive hand writing

3.      Make a column on the right hand side, if you need to do any rough work

4.      Leave two lines where you finished yesterday’s work and draw a horizontal line

5.      Write today's date on the line after that.

6.      Pending Queries from yesterday (if any).......

7.      Please write the learning outcomes as mentioned below

I will be able to  :

· recall that any real number has a decimal expansion.

· Visualize the representation of 2.665 on the number line.

 So, let's start with a quick revision of rational number on the number line.

 Now let us see how to locate 2.665 on the number line

Click on the link given below.

https://www.youtube.com/watch?v=dJkwElt-mfM&t=154s    

               

Visualize the representation of  5.3777 by successive magnification.

See this video↓

https://unacademy.com/lesson/representing-real-numbers-on-number-line/RROF1QM5

Now you are able to do Exercise 1.4

1) Visualize 3.765 on the number line using successive magnification.

Step 1: Since the given number lies between 3 and 4, look at the portion of the number line between 3 and 4.
Step 2: Divide the portion between 3 and 4 into 10 equal parts and mark each point of the division as shown in Fig. 1.
Step 3: The 7th mark and 8th mark of this sub-division corresponds to 3.7 and 3.8 respectively and 3.765 lies between them (3.7 < 3.765 < 3.8)
Step 4: Again divide the portion between 3.7 and 3.8 into 10 equal parts. Now 3.765 lies between its 6th and 7th mark (3.76 < 3.765 < 3.77) .
Step 5: Divide the portion between 3.76 and 3.77 again into ten equal parts. Therefore, the 5th mark of this sub-division mark represents 3.765 as shown in fig.3

For representation of real numbers on number line, use the following steps:
Represent √x on number line.
Step 1 Draw a line and mark a point A on it.
Step 2 Mark a point B on the line drawn such that AB = x cm.
Step 3 Mark a point C on AB produced such that BC = 1 cm.
Step 4 Find mid-point of AC (x+1). Let the mid-point be O.
Step 5 Taking O as centre and OC = OA [(x+1)/2] as radius draw a semi-circle. Also draw a line passing through B perpendicular to OB. Let it cut the semi-circle at D
Step 6 Taking B as the centre and BD as radius draw an arc cutting OC produced at E.
Point E so obtained represents √x.

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Let us solve Ex.1.5 Question 4

 Represent √(9.3) on the number line.

Step 1 Draw a line and mark a point A on it.
Step 2 Mark a point B on the line drawn such that AB = 9.3cm.
Step 3 Mark a point C on AB produced such that BC = 1 cm.
Step 4 Find mid-point of AC (9.3+1). Let the mid-point be O.
Step 5 Taking O as center and OC = OA [10.3/2] as radius draw a semi-circle. Also draw a line passing through B perpendicular to OB. Let it cut the semi-circle at D
Step 6 Taking B as the center and BD as radius draw an arc cutting OC produced at E.
Point E so obtained represents √(9.3).

Now , you can attempt Q2 of Ex 1.4 2 as H.W

AQAD

The rational number 0.3333333333……. can also be written as

      (a)   0.3

(b)   3/10

(c)   1/3

That is  all for today !

Good morning and thank you boys !

Revise the work done in class today! 

We are sure you will take all precautions to take care of yourself and your surroundings. It is of utmost importance right now. Do write the SDG -3, Good health and well being.

See you tomorrow for the next class!