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.
![Page 1: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/1.jpg)
Calculus Project 1.2
By Dorothy McCammon, Tammy Boals, George Reeves, Robert
Stevens
![Page 2: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/2.jpg)
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.
![Page 3: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/3.jpg)
Terminating Decimal Terminating decimals are decimals that
don’t continue infinitely.
![Page 4: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/4.jpg)
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.
![Page 5: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/5.jpg)
Repeating Decimal• Repeating decimals
are decimal values that never end; they just continue to repeat the same values.
![Page 6: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/6.jpg)
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.
![Page 7: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/7.jpg)
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.
![Page 8: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/8.jpg)
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.
![Page 9: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/9.jpg)
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?
![Page 10: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/10.jpg)
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.
![Page 11: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/11.jpg)
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.
![Page 12: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/12.jpg)
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
![Page 13: Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens.](https://reader036.fdocuments.us/reader036/viewer/2022082419/5a4d1b787f8b9ab0599b7fa5/html5/thumbnails/13.jpg)
• Next we do 1000r – r = 3135.135135
note that r = 3.135135 We now have 999r = 3132 so r = 3132/999 = 226/37