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)

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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