Question

Convert 0.7¯¯¯ to a fraction.

Show your work.

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

Answer 1

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

1. Let \(x = 0.7777...\)

2. Since the decimal part repeats every one digit, we can multiply \(x\) by 10 to shift the decimal point one place to the right:
\[
10x = 7.7777...
\]

3. Now, we have two equations:
\[
x = 0.7777... \quad (1)
\]
\[
10x = 7.7777... \quad (2)
\]

4. Next, we can subtract equation (1) from equation (2):
\[
10x - x = 7.7777... - 0.7777...
\]
Simplifying this gives:
\[
9x = 7
\]

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

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