Question

The fraction that is equivalent to 0.6(reapeating decimal) is

Answer 1

To convert the repeating decimal \(0.6\) (where \(6\) repeats indefinitely) into a fraction, we can use the following algebraic approach:

Let \(x = 0.666...\).

Then, we can multiply both sides of the equation by \(10\) (since there's one digit that repeats):

\[
10x = 6.666...
\]

Now, we can subtract the original equation from this new equation:

\[
10x - x = 6.666... - 0.666...
\]

This simplifies to:

\[
9x = 6
\]

Now, solve for \(x\):

\[
x = \frac{6}{9}
\]

We can simplify this fraction:

\[
x = \frac{2}{3}
\]

Thus, the fraction that is equivalent to the repeating decimal \(0.666...\) is \(\frac{2}{3}\).