write 0.6 repeated indefinitely as a fraction

Answer 1

To express 0.6 repeated indefinitely as a fraction, we can denote it as "0.666...".

Let's call the number x:
x = 0.666...

To get rid of the decimal, we can multiply both sides of the equation by 10:
10x = 6.666...

Now, subtract the original equation from the equation obtained by multiplying by 10:
10x - x = 6.666... - 0.666...
9x = 6

Divide both sides by 9:
x = 6/9

Simplifying the fraction, we find:
x = 2/3

Therefore, 0.6 repeated indefinitely can be written as the fraction 2/3