Pre Algebra Period 1

How to Change repeating decimals to fractions

Step 1: set up "n = the repeating decimal
Step 2: determine how many numbers are under the bar
Step 3: use that number as a power of 10
Step 4: multiply both sides of the equation in Step 1 by that power of 10
Step 5: Rewrite the equations so that you subtract the 1st equation FROM the 2nd equation
Step 6: Solve as a 1 or 2-step equation
Step 7: simplify, if necessary

REMEMBER-- SOMETIMES YOU NEED TO GET THE DECIMAL OUT OF THE NUMERATOR--> MULTIPLY BOTH THE NUMERATOR AND THE DENOMINATOR BY A POWER OF 10


example:
change .416666... into a fraction
let n = .416666...
notice there is one 1 number that is repeating so it is only 10 to the 1st power
multiply both sides by 10
10n = 4.16666....
now subtract the 1st equation

10n = 4.16666...
-n = 0.41666...
9n = 3.75

divide both sides by 9
9n = 3.75
9 9

or 9n/9 = 3.75/9

move the decimal 2 places in both the numerator and denominator
n = 375/900
simplify
n = 5/12

LEARN THE MOST COMMON ONES BY HEARS
Need to know:
1/9 family
1/11 family
Easy trick to recall
If the repeating decimal starts repeating right after the decimal, you can easily get the fraction just by putting the same number of 9's as the length of the repeating decimal.. then simplify:
Examples:
.4444... = 4/9
.454545.... = 45/99 = 5/11
.162162162... = 162/999 = 18/111