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Converting
Between Decimals, Percentages refer to fractions of a whole; that is, whatever you're looking at, the percentage is how much of the whole thing you have. For instance, "50%" means " 1/2 "; "25%" means " 1/4 "; "40%" means " 2/5 "; et cetera. Often you will need to figure out what percentage of something another thing is. For instance, if a class has 26 students, and 14 are female, what percentage of the students are female? It is 14 out of 26, or 14/26 = 0.538461538462..., or about 54%. (For more information on percent word problems, look at the Percent of lesson.) "Percent" is actually "per cent", meaning "out of a hundred". (I think it's Latin.) You can use this fact, along with the fact that fractions mean division, to convert between fractions, percents, and decimals. Percent to Decimal Percent-to-decimal conversions are easy; you mostly just move the decimal point two places. The way I keep it straight is to remember that 50%, or one-half, of a dollar is $0.50. In other words, you have to move the decimal point two places to the left when you convert from a percent (50%) to a decimal (0.50). Some more examples are: 27% = 0.27
Percent to Fraction Percent-to-fraction conversions aren't too bad. This is where you use the fact that "percent" means "out of a hundred". Convert the percent to a decimal, and then to a fraction. For instance:
Now you can reduce the fraction: Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved
Most conversions are simple like this, but some require a little extra care. The reason I converted to a decimal first is that the number of decimal places tells me how many zeroes to have underneath. Notice that "0.40" can also be written as "0.4". Then 0.4 = 4/10 = 2/5, which is the same answer as before. It works out because "0.40" has one decimal place and "10" has one zero. This concept helps in more complicated problems:
Another example:
If you have a graphing calculator, you can probably have the calculator do this conversion for you. Check your manual. Decimal to Fraction The technique I just demonstrated lets you convert any terminating decimal to a fraction. ("Terminating" means "it ends", unlike, say, the decimal for 1/3, which goes on forever. A non-terminating AND NON-REPEATING decimal CANNOT be converted to a fraction, because it is an "irrational" (non-fractional) number. You should probably just memorize some of the more basic repeating decimals, like 0.33333... = 1/3 and 0.666666... = 2/3. Check out the table on the last page.) Any terminating decimal can be converted to a fraction by counting the number of decimal places, and putting the decimal's digits over 1 followed by the appropriate number of zeroes. For example:
In the case of a repeating decimal, the following procedure is often used. Suppose you have a number like 0.5777777.... This number is equal to some fraction; call this fraction "x". That is: x = 0.5777777... There is one repeating digit in this decimal, so multiply x by "1" followed by one zero; that is, multiply by 10: 10x = 5.777777... Now subtract the former from the latter:
That is, 9x = 5.2 = 52/10 = 26/5. Solving this, we get x = 26/45. (You can verify this by plugging "26 ÷ 45" into your calculator and seeing that you get "0.5777777..." for an answer.) If there had been, say, three repeating digits (such as in 0.4123123123...), then you would multiply the x by "1" followed by three zeroes; that is, you would multiply by 1000. Then subtract and solve, as in the above example. And don't worry if you have leading zeroes, as in "0.004444..."; the procedure will still work. Top | 1 | 2 | 3 | Return to Index Next >>
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Copyright © 2006-2008 Elizabeth Stapel | About | Terms of Use |
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