Question

(a) What is 0.36 repeating 36 expressed as a fraction in simplest form? (b) What is 0.36 repeating 6 expressed as a fraction in simplest form? (c) What is expressed 0.36 as a fraction in simplest form?
Please help

Answer 1

A. 4/11
b. 11/30
c. 9/25

Answer 2

Answer:

a) $x=\frac{4}{11}$    

b) $x=\frac{11}{30}$  

c) $x=\frac{9}{25}$  

Step-by-step explanation:

(a) Given : 0.36 repeating 36

To find : What is 0.36 repeating 36 expressed as a fraction in simplest form?

Solution :

Let $x=0.36363636363.....$   ......(1)

Now as there are two digits repeating immediately after decimal point, we multiply above by  100  and get,

$100x=36.36363636....$  .....(2)

Subtract equation (1) from (2),

$99x=36$

$x=\frac{36}{99}$

$x=\frac{4}{11}$    

(b) Given : 0.36 repeating 6

To find : What is 0.36 repeating 6 expressed as a fraction in simplest form?

Solution :

Let $x=0.3666666.....$   ......(1)

Now as there are one digits repeating immediately after decimal point, we multiply above by  10  and get,

$10x=3.6666666....$  .....(2)

Subtract equation (1) from (2),

$9x=3.3$

$x=\frac{3.3}{9}$

$x=\frac{11}{30}$  

(c) Given : 0.36

To find : What is expressed 0.36 as a fraction in simplest form?

Solution :

Let $x=0.36$

$x=\frac{36}{100}$

$x=\frac{9}{25}$