Question

convert 0.7¯¯¯¯¯ to a fraction

Answer 1

To convert the repeating decimal \( 0.7\overline{7} \) (which means \( 0.7777...\)) to a fraction, let's denote it as \( x \):

\[
x = 0.7777...
\]

Now, to eliminate the repeating part, we can multiply both sides of the equation by 10:

\[
10x = 7.7777...
\]

Next, we can express the repeating decimal on the right side in terms of \( x \):

\[
10x = 7 + 0.7777...
\]
\[
10x = 7 + x
\]

Now, we can solve for \( x \):

\[
10x - x = 7
\]
\[
9x = 7
\]
\[
x = \frac{7}{9}
\]

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

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