Convert 0.6¯¯¯

Question

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 \( \frac{2}{3} \).