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Converting Between Decimals, Fractions, and Percents (page 2 of 4) Sections: Percent to Decimal, Percent to Fraction, Decimal to Fraction, Decimal to Percent, Fraction to Decimal, Fraction to Percent, Tables of Equivalents 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 nonterminating AND NONREPEATING decimal CANNOT be converted to a fraction, because it is an "irrational" (nonfractional) 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. Decimaltopercent conversions are simple: just move the decimal point two places to the right. (Remember, $0.50 is onehalf, or 50%, of a dollar.) For example: 0.23 = 23%
(Note that 0.97% is less than one percent. It should not be confused with 97%, which is 0.97 as a decimal.) If you remember that fractions are division, then this is easy. The calculator can do the work for you, because you can just have it do the division. For example: The bar is placed over the repeating digits, for convenience sake. When converting fractions to decimals, you may be told to round to a certain place or to a certain number of decimal places. For instance, looking at that last example, ^{2}/_{7} as a decimal rounded to the nearest tenth (rounded to one decimal place) is 0.3; to the nearest hundredth (to two decimal places) is 0.29; to the nearest thousandths (to three decimal places) is 0.286; to the nearest tenthousandths (to four decimal places) is 0.2857; et cetera. If you're not sure how you should format your answer, then give the "exact" form and the rounded form: Note that the rounded form can be useful for word problems, where a final answer in rounded form may be more practical than a repeating decimal. << Previous Top  1  2  3  4  Return to Index Next >>



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