Question

How do you write 0.083(dash over 3) as a fraction

Answer 1

To convert \( 0.083\overline{3} \) (where the 3 is repeating) into a fraction, we can follow these steps:

1. Let \( x = 0.0833333\ldots \)

2. To eliminate the repeating decimal, multiply \( x \) by 10, since the repeating part is one digit long:
\[
10x = 0.8333333\ldots
\]
(which is \( 0.08 + 0.75 = 0.08 + 0.75 = 0.08333\ldots \))

3. Now we have:
\[
x = 0.0833333\ldots
\]
\[
10x = 0.8333333\ldots
\]

4. Subtract the first equation \( x \) from the second \( 10x \):
\[
10x - x = 0.8333333\ldots - 0.0833333\ldots
\]
\[
9x = 0.75
\]

5. Solve for \( x \):
\[
x = \frac{0.75}{9}
\]
\[
x = \frac{75}{900}
\]
\[
x = \frac{1}{12}
\]

Thus, \( 0.083\overline{3} \) can be written as the fraction \( \frac{1}{12} \).