Question

Convert 0.7¯¯¯¯¯ to a fraction

Answer 1

To convert the repeating decimal \( 0.7\overline{7} \) to a fraction, we can use the following method:

Let \( x = 0.77777...\).

1. Multiply both sides of the equation by 10 to shift the decimal point:
\[
10x = 7.77777...
\]

2. Now, notice that the right side of this new equation (7.77777...) is the same as \( x \). Thus:
\[
10x = 7 + x
\]

3. Next, we can rearrange this equation to isolate \( x \):
\[
10x - x = 7
\]
\[
9x = 7
\]

4. Now, solve for \( x \):
\[
x = \frac{7}{9}
\]

So, the fraction equivalent of \( 0.7\overline{7} \) is \( \frac{7}{9} \).

Answer 2

the answer?

Answer 3

The decimal \( 0.7\overline{7} \) can be converted to the fraction \( \frac{7}{9} \).