how does o.5 being repeated as a fraction = 5/9

Answer 1

To show that 0.5 repeating as a fraction is equal to 5/9, we can manipulate the decimal to convert it to a fraction.

Let x = 0.5 repeating

Multiplying x by 10 (to shift the decimal point to the right once) gives:
10x = 5.5555...

Now, we can subtract x from 10x to get:
10x - x = 9x = 5.5555... - 0.5555... = 5

Therefore, x = 5/9, which means that 0.5 repeating as a fraction is equal to 5/9.