Question #4f6e2

1 Answer

Solve a two equation 1 variable system with x = the original number as one equation, and create a second equation by multiplying the first by the power of 10 that has as many zeroes as the repeating decimal.

4.bar(19) = 415/99

Explanation:

Step 1: create 1st equation x = given number

x = 4.19191919...

Step 2: create 2nd equation by multiplying 1st equation by power of 10 with as many 0's as repeating digits
Here 2 repeating digits so multiply both sides by 100

100x=419.19191919...

Step 3: subtract 1st equ from second to eliminate decimal part ( both sides)

" "100x=419.19191919...
- (" "x= " "4.19191919...)
------------------------------
" "99x=" "415

Step 4
Solve for x

x = 415/99 = 4.19191919...

The answer in form of a fraction is 415/99 .