Class 8 Mathematics Notes , Exercise 1.1, Unit-1, Real Numbers (National Book Foundation as Federal Text Board Islamabad for National Curriculum 2022 and onwards)

A.S.K. August 26, 2022

Class: 8th

Unit-1: Real Numbers

EXERCISE 1.1 

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1. Separate rational and irrational numbers in the following.

(i)      `\sqrt {9}`            (ii)    12             (iii)    `\frac {5}{9}`           (iv)    `\sqrt {8}`   
(v)    `\sqrt {100}`          (vi)    `\frac {13}{2}`            (vii)    `\sqrt {126}`       (viii)    `\frac {25}{9}`
(ix)    `\sqrt {169}`         (x)    `\sqrt {26}`


Hint: Rational numbers are terminating OR non-terminating and recurring decimals.

Hint: Irrational numbers are non-terminating and non-recurring decimals. 


Solution: 


Rational Numbers:

(i)      `\sqrt {9}` = 3 (Terminating decimal)

(ii)    12  (Terminating decimal)

(iii)    `\frac {5}{9}` = 0.5555......... (non-terminating and recurring decimal)

(v)    `\sqrt {100}` = 10 (Terminating decimal)

(vi)    `\frac {13}{2}` = 6.5 (Terminating decimal)

(viii)    `\frac {25}{9}` = 2.7777777...........  (non-terminating and recurring decimal)


(ix)    `\sqrt {169}` = 13 (Terminating decimal) 





Irrational Numbers:


(iv)    `\sqrt {8}` = 2.828427....... (non-terminating and non-recurring decimal)

(vii)    `\sqrt {126}` = 11.22497........ (non-terminating and non-recurring decimal)

(x)    `\sqrt {26}` = 5.09901..........(non-terminating and non-recurring decimal)

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2. Write the following in decimal form and state which of them are terminating and non-terminating decimals.

(i)      `\frac {4}{9}`         (ii)    `\frac {13}{20}`            (iii)    `\frac {1}{6}`           (iv)    `\frac {7}{3}`  
(v)    `\frac {9}{8}`          (vi)    `\frac {13}{8}`            (vii)    `\frac {11}{15}`       (viii)    `\frac {7}{11}`


Hint: The decimal fraction in which there are finite number of digits in its decimal part is called terminating decimal fraction. 

Hint: The decimal fraction in which there are infinite number of digits in its decimal part (ie. the digits in decimal parts are never ending) is called non-terminating decimal fraction. 


Solution: 


(i)      `\frac {4}{9}` = 0.44444.............. (Non-Terminating decimal) 

(ii)    `\frac {13}{20}` = 0.65 (Terminating decimal) 

(iii)    `\frac {1}{6}` = 0.1666666........(Non-Terminating decimal) 

(iv)    `\frac {7}{3}` = 2.3333333...... (Non-Terminating decimal) 
 
(v)    `\frac {9}{8}` = 1.125 (Terminating decimal) 

(vi)    `\frac {13}{8}` = 1.625 (Terminating decimal) 

(vii)    `\frac {11}{15}` = 0.733333....... (Non-Terminating decimal) 

(viii)    `\frac {7}{11}` = 0.636363.........(Non-Terminating decimal) 



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3. Name the types of the following fractions. State whether they are rational or irrational.

(i)      1.2578                     (ii)    0.33333....... 
(iii)    1.3414213662........     (iv)    5.142857142857.....  
(v)    2.236067977.....          (vi)    4.36363636.....
(viii)    4.123105626.....              


Solutions: 


(i)  1.2578 (Terminating fraction) -- Rational Number

(ii)  0.33333....... (non-terminating and recurring fraction) -- Rational Number

(iii)  1.3414213662........(non-terminating and non-recurring fraction) -- Irrational Number

(iv)  5.142857142857..... (non-terminating and recurring fraction) -- Rational Number

(v)  2.236067977.....(non-terminating and non-recurring fraction) -- Irrational Number

(vi)  4.36363636.....(non-terminating and recurring fraction) -- Rational Number

(viii)    4.123105626..... (non-terminating and non-recurring fraction) -- Irrational Number

   


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4. Ismah uses `\frac {1}{4}` of her monthly pay checque on utility bills and `\frac {1}{10}` of remaining for savings. If her last cheque was 6000.80. How much did she put in savings?           


Solution: 


Monthly Pay Cheque : Rs. 6000.80

Utility Bills = `\frac {1}{4}` of  Rs. 6000.80

Utility Bills = `\frac {1}{4}` ｘ  Rs. 6000.80

Utility Bills = Rs. 1500.2

Remaining Pay = Rs, 6000.80 - Rs. 1500.2 = Rs. 4500.6

Savings = `\frac {1}{10}` of  Rs. 4500.6

Savings = `\frac {1}{10}` ｘ  Rs. 4500.6

Savings = Rs, 450.06   ----------------Ans.


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5. Raiqa is decorating for a birthday party and she purchase 20.7 feet of purple ribbon. She plans to use `frac {1}{3}` of the ribbon in the drawing room and `frac {1}{2}` of remaining in dinning room. How much ribbon will she have left over.


Solution: 



Length of the purple ribbon : 20.7 feet

To use in drawing room = `\frac {1}{3}` of 20.7 feet

To use in drawing room = `\frac {1}{3}` ｘ 20.7 feet

To use in drawing room = 6.9 feet


Remaining ribbon = Total length - To use in drawing room
Remaining ribbon = 20.7 feet - 6.9 feet 
Remaining ribbon = 13.8 feet



To use in dinning room of the remaining = `\frac {1}{2}` of 13.8 feet


To use in dinning room of remaining = `\frac {1}{2}` ｘ 13.8 feet


To use in dinning room = 6.9 feet

Ribbon left over with her = Remaining after using in drawing room - using in dinning room

Ribbon left over with her = 13.6 feet - 6.9 feet 
Ribbon left over with her = 6.9 feet------Ans.


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