Question

Express following recurring decimal as fraction
Creations

0.13​

Answer 1

Answer:

$0.13 = \frac{13}{10} \\ \\ this \: \: is \: \: the \: \: answer.$

Answer 2

Step-by-step explanation:

Explanation:

First some notation:

Just in case you might not have met it, drawing a bar above a group of digits means that that sequence of digits repeats, so we can write:

0.131313

...

=

0

.

¯¯¯¯

13

Multiply by

(

100

−

1

)

to get an integer:

(

100

−

1

)

0

.

¯¯¯¯

13

=

(

100

⋅

0

.

¯¯¯¯

13

)

−

(

1

⋅

0

.

¯¯¯¯

13

)

=

13

.

¯¯¯¯

13

−

0

.

¯¯¯¯

13

=

13

Then divide both ends by

(

100

−

1

)

and simplify:

0

.

¯¯¯¯

13

=

13

100

−

1

=

13

99

Why

(

100

−

1

)

?

The multiplier

100

shifts the number two places to the left - the length of the repeating pattern. Then subtracting the original pattern cancels out the repeating tail.