Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.
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Transcript of Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.
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~ 1/6 = .16666~1/9 = .1111~ 1/11 = .0909~1/33 = .0303~ 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