Question

Write the following decimal number in its equivalent fraction form.

Answer 1

Answer:

-0.6666.... = - $\frac{2}{3}$

Step-by-step explanation:

Repeating decimals can be written as either 0.6666..., or as 0.6 with a small line over the top of the 6 to indicate it repeats.  Repeating fractions are not put into fractions in the traditional way.  If we had the terminating decimal 0.4, then we know to put the 4 over 10 and reduce:

$\frac{4}{10}=\frac{2}{5}$

However, with repeating decimals, instead of putting the number of the decimal over a value of 10, we put it over a value of 9.  So, for the equivalent fraction form of -0.6 (repeating) we would get:

$\frac{6}{9}=-\frac{2}{3}$