Question

Enter your answer as a simplified fraction formatted like this: 42/53

Answer 1

Answer:

$\displaystyle -0.\overline{37}=-\frac{37}{99}$

Step-by-step explanation:

Convert a Repeating Decimal to a Fraction

We need to convert the following decimal to a fraction:

$-0.\overline{37}$

Let's call x to the given number:

$x=-0.\overline{37}$

The number has two repeating (periodic) decimals, thus we multiply by 100:

$100x=-37.\overline{37}$

Note the decimals continue to repeat exactly like the original number.

Subtracting both expressións, the repeating decimals are simplified:

$100x - x = -37$

Operating:

99x=-37

Dividing by 99:

$\displaystyle x=-\frac{37}{99}$

The fraction cannot be simplified, thus:

$\mathbf{\displaystyle -0.\overline{37}=-\frac{37}{99}}$