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