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The
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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". (It comes from the Latin per centum for "thoroughly hundred".) You can use this "out of a hundred" meaning, along with the fact that fractions indicate 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 1999-2009 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 "0.4" has one decimal place and "10" has one zero. This concept (matching the number of decimal places with the number of zeroes) 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 © 1999-2010 Elizabeth Stapel | About | Terms of Use |
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