Represent 0 . 3 ¯ and 0 . 6 ¯ as fractions.

Given, the first number is 0 . 3 ¯ Let x = 0 . 3 ¯ . . . . . ( 1 ) Multiply both sides by 10 10 x = 0 . 3 ¯ × 10 10 x = 3 . 3 ¯ . . . . . ( 2 ) Subtracting e q ( 2 ) - e q ( 1 ) , we get 9 x = 3 x = 3 9 x = 1 3 Hence, 0 . 3 ¯ can be represented in fraction as 1 3 . Given, the second number is 0 . 6 ¯ Let y = 0 . 6 ¯ . . . . . ( 1 ) Multiply both sides by 10 10 y = 0 . 6 ¯ × 10 10 y = 6 . 6 ¯ . . . . . ( 2 ) Subtracting e q ( 2 ) - e q ( 1 ) , we get 9 y = 6 y = 6 9 y = 2 3 Hence, 0 . 6 ¯ can be represented in fraction as 2 3 .

Show that 0 . 9 ¯ = 1 by adding together 0 . 3 ¯ and 0 . 6 ¯ and then adding together their equivalent fractions which you found in step a.

In step a, we have expressed that : 0 . 3 ¯ = 1 3 . . . . . ( 1 ) 0 . 6 ¯ = 2 3 . . . . . ( 2 ) We know that, 0 . 9 ¯ = 0 . 3 ¯ + 0 . 6 ¯ From e q ( 1 ) & e q ( 2 ) , 0 . 9 ¯ = 1 3 + 2 3 0 . 9 ¯ = 1 + 2 3 0 . 9 ¯ = 3 3 ⇒ 0 . 9 ¯ = 1

Show that 0 . 9 = 1 by adding together 0 . 25 ¯ and 0 . 74 ¯ .

Given, the first number is 0 . 25 ¯ Let x = 0 . 25 ¯ . . . . . ( 1 ) Multiply both sides by 100 100 x = 0 . 25 ¯ × 100 100 x = 25 . 25 ¯ . . . . . ( 2 ) Subtracting e q ( 2 ) - e q ( 1 ) , we get 99 x = 25 x = 25 99 Hence 0 . 25 ¯ can be represented in fraction as 25 99 . Given, the second number is 0 . 74 ¯ Let y = 0 . 74 ¯ . . . . . ( 3 ) Multiply both sides by 100 100 y = 0 . 74 ¯ × 100 100 y = 74 . 74 ¯ . . . . . ( 4 ) Subtracting e q ( 4 ) - e q ( 3 ) , we get 99 y = 74 y = 74 99 Hence 0 . 74 ¯ can be represented in fraction as 74 99 . Adding 0 . 25 ¯ & 0 . 74 ¯ , 0 . 99 ¯ = 0 . 25 ¯ + 0 . 74 ¯ We know that, 0 . 99 ¯ = 0 . 9 ¯ ⇒ 0 . 9 ¯ = 0 . 25 ¯ + 0 . 74 ¯ Using value of x & y calculated above, 0 . 9 ¯ = 25 99 + 74 99 0 . 9 ¯ = 25 + 74 99 0 . 9 ¯ = 99 99 ⇒ 0 . 9 ¯ = 1 Hence proved.

E M B I B E

MYP Mathematics A concept-based approach 3>Chapter 1 - Number Discoveries and Developments>Practice 1>Q 2

MEDIUM

MYP:3

IMPORTANT

Earn 100

Represent each of the following rational numbers as a fraction in simplified form.

$12.874$

Important Questions on Number Discoveries and Developments

EASY

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 1 - Number Discoveries and Developments>Practice 1>Q 2

Represent following rational number as a fraction in simplified form.

$0.1333 . . .$

EASY

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 1 - Number Discoveries and Developments>Practice 1>Q 2

Represent the following rational number as a fraction in simplified form.

$5$

HARD

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 1 - Number Discoveries and Developments>Practice 1>Q 2

Represent each of the following rational numbers as a fraction in simplified form.

$- 4.1392$

HARD

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 1 - Number Discoveries and Developments>Practice 1>Q 2

Represent following rational number as a fraction in simplified form.

$5.6 \bar{72}$

HARD

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 1 - Number Discoveries and Developments>Practice 1>Q 2

Represent following rational number as a fraction in simplified form.

$9.03555 . . .$

MEDIUM

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 1 - Number Discoveries and Developments>Practice 1>Q 3

Represent $0 . \bar{3}$ and $0 . \bar{6}$ as fractions.

MEDIUM

MYP:3

IMPORTANT

MYP Mathematics A concept-based approach 3>Chapter 1 - Number Discoveries and Developments>Practice 1>Q 3

Show that $0 . \bar{9} = 1$ by adding together $0 . \bar{3}$ and $0 . \bar{6}$ and then adding together their equivalent fractions which you found in step a.