NUMBER SYSTEM (LECTURE 3)

LESSON 3  NUMBER SYSTEM

Dear Students,

Good morning ! 

We have covered the following learning outcomes so far:

• Recall what are natural numbers,whole numbers, integers and rational numbers.
• State the relation between different number systems.
• Recall what are rational numbers
• What are Irrational numbers
• Locating Irrational numbers on a number  line.

Any queries from Lesson -1 or 2? Then please post as comment below !!

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

·         The text in Red, is to be written in your note book

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

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

        Follow the instructions (such as write / view / recall....) as and when they appear in my blog

·         I will be with you on this blog in your maths slot so that I can address to any queries that you may have when you go through the lesson. However, if you post any query after this, I will address to that only on the next day during the Maths slot.

·         Feel free to clarify your doubts by dropping a comment before going ahead in the lesson. PLEASE DO WRITE YOUR NAME along with your query in the comment box. 🙏

1. Take your SET-A Mathematics Note Book.
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. We need to save paper. Write the SDG – 12 : Responsible Consumption and Production. Remember we contemplated on SDG-1 in yesterday’s class ? Let us be responsible global citizens. One good thing that Coronavirus is teaching us! That is, be responsible global citizens!
6. Please write the learning outcomes as mentioned below 

I will be able to

• Recall what are rational numbers / irrational numbers    
• Find rational number(s)  between given numbers
• Find irrational number(s)  between given numbers

Click on the following link 👇 to answer few questions:

NUMBER SYSTEM QUIZ  (self assessment)

Thank you for taking that quiz.

Your answers will reach me directly.

Hope you have written the feedback in your note books for your self. (it was given with your assessment score)

Now let us practice a little more : Write in your note books

Complete the following statements:

Q1)The decimal representation of a rational number may be __________ or ________.

Q2) The actual value of p is ___________ but we take it as ________ or _______ for our convenience.

Please give your responses in the comments below. Once I get the correct response, I will not take further response for the same question. So, all the please read the comments for correct response for Q1 and Q2

Q3) Find three rational numbers between 1/7 and 2/9

A3)  Step 1:  LCM of "7" and "9" is ______

        

        Step 2:  1/7 = _____  { Hint: the LCM that you found in step 1 should be the                                   denominator of your answer in this step. Use the concept of equivalent fraction}

        Step 3:  1/9 = _____  { Hint: same as above}

        Step 4:  the  required three no.s are ____ , ____, _____

{ Hint: since the denominator is same for the answers in step 2 and step 3, find the numbers between the two numerators and write them with the LCM, that you found in step 1 as their denominators}

Q4) Find three rational numbers between (-2/3) and (-4/9). 

      { Hint: follow the same procedure as in Q3}

Q5) Find three irrational numbers between 1/7 and 2/9

A5)  Step 1:  1/7 = _____  { Hint: divide 1 by 7 and write till 3 decimal places}

        Step 2:  1/9 = _____  { Hint: divide 1 by 9 and write till 3 decimal places}

        Step 3:  the  required three no.s are ____ , ____, _____

{ Hint: write three numbers between the answers in step 2 and step 3. Ensure your answer is non terminating (HOW ? it should end with ......) and it should be non recurring (HOW ? make sure the digits don not repeat after another }

Q6) Find three irrational numbers between (-2/3) and (-4/9). 

      { Hint: follow the same procedure as in Q5}

Now you will be able to do Q1, 2, 5, 7, 8 ,9 from Ex. 1.3 of NCERT

Students, please click on the following link👇 

CONVERT DECIMAL to p/q form

Q7) By the way 1.33.... can also be written as _____  (view the image below to answer)

Q8) Express 1.33........ in the form p/q, where p & q are Z, q ≠ 0

A8) Step -1 :   Let  1.33.... = n      →  (equation 1)   {Hint: making an assumption}

       Step -2 :   13.33....     = 10n    →  (equation 2) {Hint: multiply both sides by 10, 
                                                            why ? because only one digit "3" is repeating}

       Step -3 : 12 = 9n      →  (equation 2 - equation 1)   {Hint: the decimal part in both
                                                            the equation (1) and (2) is same (33....) , so it 
                                                                                       vanishes}
       
       Step -4 : 12 /9  = n   {Hint: making "n" alone, by dividing both sides by 9}
        
       Step -5 : 4 /3  = n   {Hint: reduce to lowest terms}

        Answer = 4/3 👍

Q9) Express 2.4747........ in the form p/q, where p & q are Z, q ≠ 0

A8) Step -1 :   Let  2.4747...... = n      →  (equation 1)   {Hint: making an assumption}

       Step -2 :   247.4747....     = 100n    →  (equation 2) {Hint: multiply both sides by 100, 
                                                            why ? because only two digits "47" are repeating}

       Step -3 : 245 = 99n      →  (equation 2 - equation 1)   {Hint: the decimal part in both
                                                            the equation (1) and (2) is same (4747....) , so it 
                                                                                       vanishes}
       
       Step -4 : 245 /99  = n   {Hint: making "n" alone, by dividing both sides by 99}
        
          {Hint: already in lowest terms}

        Answer = 245 /99 👍

Now you will be able to do Q3 from Ex. 1.3 of NCERT

I will be sending you few more questions for practice through whatsapp group as a worksheet !

Good morning and thank you boys !

Take a good care of yourself!

See you on 7th April, Day -4, for the next class !