How do you convert 0.83 (3 repeating) to a fraction?

To convert the repeating decimal 0.83 (with 3 repeating) to a fraction, we can follow these steps:

1. Let x equal the repeating decimal:

   Let x = 0.83333…

2. Multiply by a power of 10:

   To eliminate the repeating part, multiply x by 10 to shift the decimal point to the right:
   
   x = 0.83333… (1st equation)
   
   10x = 8.3333… (2nd equation)

3. Subtract the two equations:

   Now we’ll subtract the 1st equation from the 2nd:
   
   10x – x = 8.333… – 0.833…
   
   9x = 7.5

4. Solve for x:

   Now divide both sides by 9:
   
   x = 7.5 / 9

5. Simplify the fraction:

   To simplify 7.5 / 9, we can multiply the numerator and the denominator by 10 to remove the decimal:
   
   x = 75 / 90

   Next, simplify 75 / 90:
   
   75 ÷ 15 = 5
   
   90 ÷ 15 = 6

   Thus, the simplest form of the fraction is:

   x = 5/6

Therefore, the repeating decimal 0.83 (3 repeating) can be expressed as the fraction 5/6.