# How do you convert 1.37 (7 being repeated) to a fraction?

Mar 17, 2016

$\frac{62}{45}$

#### Explanation:

We first let 1.37 (7 being repeated) be $x$.

Since $x$ is recurring in 1 decimal places, we multiply it by ${10}^{1}$.

$10 x = 13.77$

Next, we subtract them.

$10 x - x = 13.77 - 1.37$

$9 x = 12.4$

Lastly, we divide both sides by 9 to get $x$ as a fraction.

$x = \frac{12.4}{9}$

$= \frac{124}{90}$

$= \frac{62}{45}$

Mar 18, 2016

Let $x = 1.377777777 \ldots .$, then

$10 x = 13.77777777 \ldots$ and
$100 x = 137.777777777 - - -$

Subtracting 2nd equation from third, we get

$90 x = 124$

$x = \frac{124}{90} = \frac{62}{45}$

Mar 18, 2016

x=45/62

#### Explanation:

$$_


1.37
x=1.37
10x=13.7
100x=137.7
100x-10x=137.7-13.7
90x=124
x=124/90
x=45/62