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

a)
`x=(4)/(11)`

b)
`x=(11)/(30)`

c)
`x=(9)/(25)`

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=(36)/(99)`

`x=(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=(3.3)/(9)`

`x=(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=(36)/(100)`

`x=(9)/(25)`