Question

prove algebraically that 0.5 recurring is 5/9
please help thank you

Answer 1

Answer:

Suppose x=0.555\ldotsx=0.555… . Then 10x=5.555\ldots10x=5.555… . Subtracting xx from 10x10x will drop the fractional part:

10x-x=9x=5.555\ldots-0.555\ldots=510x−x=9x=5.555…−0.555…=5

from which we immediately get x=\dfrac59x=

9

5