5. Creating Integers: Explore the relationship between a fraction and its decimal
equivalent. (40 points – 10 pts each)
Initial Analysis or Plan: Briefly analyze the problem and your plan for solving it.
This problem deals with integers that are being multiplied by decimals producing
various results as detailed below.
a. What is the smallest positive integer that will "work"?
b. What are the smallest positive integers that will work for other decimals such as
0.05, 1.25, 0.375, 0.444...,
?
c. Compare your answers with the fraction equivalents of 0.20, 0.05, 1.25, 0.375,
0.444.... and
. Describe how a fraction equivalent can be determined from
a decimal number.
Will this method work for all decimal numbers? Why? Why Not?
I filled in the numbers in Excel up to just over 5000. I then filled in what each
corresponding column would be based on numbers provided.
Attempted Solution: Carry out your plan and write up a solution
a.)
b.)
c.)
d.)
The smallest positive integer being multiplied by .2 and resulting in an integer
solution is 5.
For .05 smallest integer is 20. For 1.25 smallest integer is 4. For .0375
smallest integer is 8. For .444 the smallest integer is 500. For 0.142857 the
smallest integer is 7.
If I understand correctly nothing changes. I simply plugged them in as
fractions for example .20 I used 20/100 instead.
I think that this method should work for all decimals as long as it is rational.
An example where it won’t work is pi. Pi is irrational it never ends. However
with some rounding and approximation you may be able to get a whole
number.
Closing Analysis:

Analyze the activities from the learning window; usefulness for learning the
content?
Overall an entertaining activity that was not too hard based on the student’s
level of Excel experience. It demonstrates that multiplying by a decimal and a
fraction are on in the same.

Analyze the activities from the teaching window, usefulness for teaching the
content?
This is a very useful activity and one I would use in my classroom as an
extension.
Final Personal Reflections:
I enjoyed this activity. Excel is great in that it save a lot of time and
requires little effort if you are decent at navigating it. This would be a
great activity for all levels of mathematics.