Answer:
[tex]\displaystyle -0.\overline{37}=-\frac{37}{99}[/tex]
Step-by-step explanation:
Convert a Repeating Decimal to a Fraction
We need to convert the following decimal to a fraction:
[tex]-0.\overline{37}[/tex]
Let's call x to the given number:
[tex]x=-0.\overline{37}[/tex]
The number has two repeating (periodic) decimals, thus we multiply by 100:
[tex]100x=-37.\overline{37}[/tex]
Note the decimals continue to repeat exactly like the original number.
Subtracting both expressións, the repeating decimals are simplified:
[tex]100x - x = -37[/tex]
Operating:
99x=-37
Dividing by 99:
[tex]\displaystyle x=-\frac{37}{99}[/tex]
The fraction cannot be simplified, thus:
[tex]\mathbf{\displaystyle -0.\overline{37}=-\frac{37}{99}}[/tex]
