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