Question

Write 0.583(repeating on 3)as a rational number. Please explain this is complicated

Answer 1

not complicated at all. Any group of n repeating digits (.ddd) can be represented by ddd/999 where there are as many 9's as digits. So,

0.583 = 583/999

To see why this is so, consider what happens if you assign the value to a variable, say x:

x = 0.583583583...

Now, shift the decimal point by 3 places (the number of digits):

1000x = 583.583583583...

Now subtract, and the factional part disappears

1000x-x = 583.0000000...

999x = 583
x = 583/999