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Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens Part 1 • When you have a fraction x/y, y can be divided into x to obtain that fraction in decimal form. • There are two different types of decimal numbers you can obtain. Terminating Decimal Terminating decimals are decimals that don’t continue infinitely. Examples of Terminating Decimals 1/2 = .5; 1/5 = .2; 1/10 = .1 1/4 = .25; 1/25 = .04; 1/125 = .008 1/625 = .0016; 1/2500 = .0004 Note that all of these values end; they don’t continue with a repeating decimal value. Repeating Decimal • Repeating decimals are decimal values that never end; they just continue to repeat the same values. Examples of Repeating Decimals 1/3 = .3333~ 1/9 = .1111~ 1/33 = .0303~ 1/6 = .16666~ 1/11 = .0909~ 1/99 = .010101~ Note that these values are never-ending. They will continue to repeat. How can one tell which type of decimal they’ll get? • It’s very simple. As long as the denominator is made of the numbers (2^x)(5^y) where x and y are nonnegative integers, the value will be terminating. Examples • 1/(2^3)(5^4) = .0002 1/(2^5)(5^6) = .000002 1/(2^2)(5^3) = .002 All of these values are terminating. Decimal to fraction Part 2 • If you are given a decimal instead of a fraction, how can you make it a fraction when it is either terminating or repeating? Terminating into a fraction • Terminating decimals are easy to turn into fractions. You can just put the value over 10,100,1000, etc; the denominator depends on the decimal place. Examples • .1 = 1/10 .01 = 1/100 .001 = 1/1000 .0001 = 1/10000 .5 = 5/10 = 1/2 .25 = 25/100 = 1/4 These values are easy to convert. Making the new fraction is very simple. Repeating into fraction • Converting repeating decimals is a bit more complicated. Let’s take 3.135135 for example. We can set it equal to r: r = 3.135135 There are 3 repeating values so we will set it equal to 1000r = 3135.135135 • Next we do 1000r – r = 3135.135135 note that r = 3.135135 We now have 999r = 3132 so r = 3132/999 = 226/37