Question

How do you write 0.94(dash over 4) as a fraction

Answer 1

To convert the repeating decimal \( 0.94\overline{4} \) (which means the digit \( 4 \) repeats infinitely) into a fraction, we can use algebraic methods.

Let's denote \( x = 0.94\overline{4} \):

1. **Multiply by 10** to shift the decimal point:
\( 10x = 9.44\overline{4} \)

2. **Multiply by 100** to shift the decimal point two places:
\( 100x = 94.44\overline{4} \)

3. **Subtract the first equation from the second** to eliminate the repeating part:

\[
100x - 10x = 94.44\overline{4} - 9.44\overline{4}
\]

This simplifies to:

\[
90x = 94.44 - 9.44
\]

Calculating the right side:

\[
90x = 85
\]

4. **Solve for \( x \)**:

\[
x = \frac{85}{90}
\]

5. **Simplify the fraction**:

Both the numerator and denominator can be divided by 5:

\[
x = \frac{17}{18}
\]

Thus, the fraction representation of \( 0.94\overline{4} \) is \( \frac{17}{18} \).