Notes Converting Between Decimals, Fractions, and Percents Fraction to Decimal Remember that fractions are division. For example: Try these examples: 3 = 4 2 = 7 Percent to Decimal 27 If percent means “out of one hundred” then 27% means 27 out of 100 or so 0.27. Divide the percent by one 100 hundred for the equivalent decimal. Try these examples: 104% = 0.5% = Decimal to Percent Multiply the decimal by one hundred. For example: 0.23 = 0.23 × 100 = 23%. Try these examples: 2.34 = 0.0097 = Terminating Decimal to Fraction Any terminating decimal can be converted to a fraction by counting the number of decimal places, and putting the 25 5 decimal's digits over a multiple of ten. For example 2.5 = . 10 2 Try these examples: 1.5 = 10.2 0.0003 = Percent to Fraction Use the fact that "percent" means "out of a hundred". Convert the percent to a decimal, and then to a fraction. For 40 40 4 2 example 40% = 0.40 = then reduce . 100 100 10 5 ©Dr Barbara Boschmans 1/5 Notes Try these examples: 104% = 0.5% = 1 33 % = 3 1 12 % = 2 Non-terminating, Repeating Decimal to Fraction In the case of a non-terminating, repeating decimal, the following procedure is used. Suppose you have a number like 0.333333.... This number is equal to some fraction; call this fraction "x". That is: Let x = 0.333333... There is one repeating digit in this decimal, so multiply x by 10 to bring one repeating part in front of the decimal: Then 10 x = 3.33333... Subtract: 10 x = 3.33333... - x = 0.33333... 9 x = 3 3 1 So x = 9 3 1 You might have already known that 0.3 from previous experiences, but it is an example to show you the 3 procedure of converting a non-terminating, repeating decimal to a fraction. Let’s do another example: Suppose you have a number like 0.5777777.... This number is equal to some fraction; call this fraction "x". That is: Let x = 0.5777777... There is one repeating digit in this decimal, so multiply x by 100 to bring the non-repeating part and the repeating part in front of the decimal: Then 100 x = 57.77777... Subtract: 100 x = 57.777777... - 10 x = 5.7777777... [Remember: your goal is to eliminate the repeating decimal part so 90 x = 52 subtracting x would not do this, but subtraction 10 x will!] Then 90 x = 52 52 26 So x = 90 45 ©Dr Barbara Boschmans 2/5 Notes Try these examples: 0.777777….. = 0.2525252525…. = 2.345345345…. = 0.45666666…. = 0.00022222…. = ©Dr Barbara Boschmans 3/5 Notes Fraction to Percent Convert to a decimal and then to a percent if you have a terminating decimal. For example: Try these examples: 3 = 2 5 = 8 For non-terminating decimals you use a fraction inside the percent. For instance: So 0.38888888… = 38.888888…%. The goal is to convert 0.888888… to a fraction, using the technique of converting non-terminating, repeating decimals to fractions. Let x = 0.888888... There is one repeating digit in this decimal, so multiply x by 10 to bring one repeating part in front of the decimal: Then 10 x = 8.88888... Subtract: 10 x = 8.88888... - x = 0.88888... 9 x = 8 8 So x = 9 7 8 So the final answer: 38 % 18 9 Here's a messier example: This is non-terminating, so 0.5428571428571… = 54.28571428571% and you want to convert the 0.2857142857 to a fraction. You can also do this by decimal long division: Note that the remainder is 10 and the divisor is 35, so the decimal answer is: ©Dr Barbara Boschmans 4/5 Notes Try these examples: 89 = 37 297 = 81 421 = 23 ©Dr Barbara Boschmans 5/5 .