Question

How is 0.136¯ written as a fraction in simplest form? Enter your answer in the box.

Answer 1

The answer is 3/22
I see the answer 17/125 around a lot, and that's not wrong but I don't think it's simplified enough

Answer 2

Answer:

$0.13\bar{6}$ as fraction $\dfrac{41}{300}$

Step-by-step explanation:

We are given a repeating decimal number.

$0.13\bar{6}$

We need to change into fraction.

Repeating decimal means number repeat infinite number of times.

So, we can write $0.13\bar{6}$ = 0.1366666666..............

Let,

$x=0.1366666666.......$

Multiply both sides by 100

$100x=13.66666666.......-------------(1)$

Multiply both sides by 10

$1000x=136.66666666......-------------(2)$

Subtract eq(2) - eq(1)

$1000x-100x=136.666666.... - 13.666666....$

$900x=123$

$x=\dfrac{123}{900}=\dfrac{41}{300}$

Hence, $0.13\bar{6}$ as fraction $\dfrac{41}{300}$