Question

Solve and show your work for each question.
(1) What is 0.36 repeating expressed as a fraction in simplest form?
(2) What is 0.36 only 6 repeating expressed as a fraction in simplest form?
(3) What is 036 expressed as a fraction in simplest form?

Answer 1

THE ANSWER FOR QUESTION 1.  Answer:

0.363636363636..................=411

Explanation:

Le x=0.363636363636..................

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

100x=36.363636363636..................

Now subtracting first equation from second we get

99x=36 and hence x=3699=9×49×11=411

THE ANSWER FOR QUESTION 2.Answer:

To find out what is 0.36… as a fraction, identify the repeating sequence or pattern, known as reptend or repetend of 0.36 recurring.

The infinitely-repeated digit sequence of 0.36… can be indicated by three periods. For example, 0.3666… as a fraction (repeating 6, the last digit) = 11/30 .

Alternatively, a vinculum, that is a horizontal line, can be drawn above the repetend of the fraction of 0.36. In addition, one can sometimes see the period enclosed in parentheses ().

Here, we use the overlined notation to denote 0.36 repeating as a fraction:

0.36 = 11/30 
0.36 = 4/11

These results for 0.36 repeating as a fraction are approximations and limited to three digits fractions. For different periods, higher precision and more results use the calculator below

 

THE ANSWER FOR QUESTION 3.  Step 1: 0.36 = 36⁄1000 
Step 2: Simplify 36⁄1000 = 9⁄250  

Answer 2

Answer:

Part 1).

let, $x=0.\overline{36}$

x = 0.363636...    _______(1)

multiply both sides by 100, we get

100x = 36.363636... ______(2)

Subtract equation (1) from (2),

100x - x = ( 36.363636... ) - ( 0.363636... )

99x = 36

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

$x=\frac{12}{33}$

Therefore, $0.\overline{36}$ in simplest form is $\frac{12}{33}$.

Part 2).

let, $x=0.3\overline{6}$

x = 0.3666...    _______(1)

multiply both sides by 10, we get

10x = 3.6666... ______(2)

Subtract equation (1) from (2),

10x - x = ( 3.6666... ) - ( 0.3666... )

9x = 3.3

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

$x=\frac{33}{90}$

$x=\frac{11}{30}$

Therefore, $0.3\overline{6}$ in simplest form is $\frac{11}{30}$.

Part 3).

let, $x=0.36$

In fraction, we get

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

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

Therefore, $0.36$ in simplest form is $\frac{9}{25}$.