Question

Convert 0.6¯¯¯
to a fraction, reduced to lowest terms.(1 point)
The fraction that is equivalent to 0.6¯¯¯
is

Answer 1

Let \( x = 0.6666\ldots \) (where the 6s are repeating). To convert this repeating decimal into a fraction, we can follow these steps:

1. **Multiply \( x \) by 10** to shift the decimal point one place to the right:
\[
10x = 6.6666\ldots
\]

2. **Subtract the original \( x \) from this new equation**:
\[
10x - x = 6.6666\ldots - 0.6666\ldots
\]

This simplifies to:
\[
9x = 6
\]

3. **Solve for \( x \)**:
\[
x = \frac{6}{9}
\]

4. **Reduce the fraction**:
\[
x = \frac{2}{3}
\]

Therefore, the fraction that is equivalent to \( 0.6666\ldots \) is \( \frac{2}{3} \).