Question

Question #4f6e2

Answer 1

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` .