Decimals

__**Changing Decimals to Fractions**__
by: Andrew

well i know one really easy way to change a decimal into a fraction it any number from .1-.9 is equal to that number minus the. over 10 for example .5 could be written as 5/10 enter that into a calculator and see for yourself. now what about number like .55? well its the same thing except you use 100 instead of 10 so .55=55/100 =11/20( 11/20 is the simplistic form)

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: 10//x// = 5.777777... Now subtract the former from the latter: That is, 9//x// =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.