Question

Convert 0.7¯¯¯
to a fraction.

Show your work.

(1 point)
The fraction equivalent of 0.7¯¯¯ is

Answer 1

Let \( x = 0.7\overline{7} \).

This means that \( x = 0.7777777\ldots \)

To convert this repeating decimal into a fraction, we can use the method of multiplying by a power of 10 to shift the decimal point. Since the repeating part (7) consists of only one digit, we will multiply by 10.

So, we have:

\[
10x = 7.7777777\ldots
\]

Now we can set up an equation by subtracting the original \( x \) from this new equation:

\[
10x - x = 7.7777777\ldots - 0.7777777\ldots
\]

This simplifies to:

\[
9x = 7
\]

Now, we can solve for \( x \) by dividing both sides by 9:

\[
x = \frac{7}{9}
\]

Thus, the fraction equivalent of \( 0.7\overline{7} \) is

\[
\boxed{\frac{7}{9}}.
\]