How would you convert a recurring decimal to a fraction?
With this question, it is useful to work with a specific example, so let’s take the recurring decimal 0.27. The first step in converting it to a fraction is to set it equal to x, this will help us with our algebraic manipulations.So we have x = 0.27 (rec) [1]The next step of this process is to multiply both sides of the equation by 100, we do this to draw out the first sequence of the repeating decimal, like so100x = 27.27 (rec) [2]If we were working with 0.9 recurring, we would multiply both sides by 10 and if the question referred to 0.327 recurring, we would multiply by 1000. You want to multiply both sides by 10pwhere p is the number of digits that are recurring. The next step is to subtract equation [1] from equation [2], note that on the right hand side of both equations, everything after the decimal point will cancel out in this subtraction. This leaves us with;99x = 27Then finally, divide both sides by 99 to solve for x and simplify.X = 27/99 = 3/11 = 0.27 (rec)
