Now that you have converted a terminating decimal number into a fraction, try converting a repeating decimal number into a fraction. Repeating decimal numbers are more difficult to convert into fractions. The first step is to assign the given decimal number to be equal to a variable, . For the decimal number , that means . If , what does 10x equal?
Accepted Solution
A:
The first step is to assign the decimal number to a variable.
For the repeating fraction 0.111_1, this would look like .. x = 0.111_1 . . . . . . . . . . where we use an underscore to identify the following digit(s) as repeating
The next step is to multiply that value by 10 to a power equal to the number of repeating digits. If there is one repeating digit (as here), then you want (10^1)x = 10x. .. 10x = 1.111_1
The third step is to subtract x from this. .. 10x -x = 1.111_1 -0.111_1 = 1 .. 9x = 1
And the final step is to divide by the coefficient of x. .. x = 1/9 . . . . . . this is the value of the repeating decimal fraction.
_____ Here's one that's a little more complicated. It is done the same way. .. x = 3.254545_45 .. 100x = 325.454545_45 .. 100x -x = 99x = 322.2 .. x = 322.2/99 = 3222/990 = 179/55