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Question 501039: Dear teacher,
I would like to first thank you for answering my question though you don't know me, so thanks anyway!!!!
My question is, is there any way for us students to remember the difference between rational and irrational numbers? Please remember that we would like it to be easy to remember and not complicated.
Thank you teacher again!!!!
Found 2 solutions by emargo19, Theo:
Answer by emargo19(101)   (Show Source):
You can put this solution on YOUR website! you know i know this may sound strange, but like you i am a student and the best way i remember that irrational numbers are non-recurrent is by comparing them to the shapes of the states of US that is, no state in the US looks a like...same way in irrational numbers the decimals are non-recurring(not alike).
I hope that helps.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! here's a couple of references that might help you.
http://www.themathpage.com/aPrecalc/rational-irrational-numbers.htm
http://apod.nasa.gov/htmltest/rjn_dig.html
http://online.math.uh.edu/MiddleSchool/Modules/Module_4_Geometry_Spatial/Content/IrrationalNumbers.pdf
these references address the subject in sufficient detail for you to get an idea.
the basic definition is:
a rational number is a number that can be expressed as the ratio of 2 integers.
in decimal form, a rational number will either have a finite number of decimal places, or it it has an infinite number of decimal places, there will be a repeating pattern that goes on endlessly.
some examples of rational numbers:
6/9 is a rational number
3/4 is a rational number
6.25 is a rational number because it can be expressed as 625/1000 which can be reduced to 5/8 by dividing numerator and denominator by 125.
2/3 is a rational number.
2/3 = .66666666666666666.................
the number of decimal places never ends.
the decimal places repeat every digit (6 then 6 then 6, etc).
9/11 is a rational number.
9/11 = .818181818181818181.....................
the number of decimal places go on endlessly.
the decimal places repeat every other digit (81 then 81 then 81, etc).
some well known irrational numbers are:
pi = 3.141592654.........
e = 2.718281828....................
the number of decimal places go on endlessly.
the decimal places do not have a repeating pattern.
pi shows no pattern from the beginning.
e looks like it has a pattern, but when you get past the 10th decimal place the repetitive pattern stops and there is no further repetition as you get further out.
those are the 2 main tests.
some number are easy to determine.
others are move difficult because they might be rational but the number of digits might be greater than the calculator can show, or they might have a repeating pattern that is larger than the calculator can show.
for the most part, irrational numbers are dealt with by carrying out the calculations to a degree of accuracy greater than that required. this insures that the accuracy will be what you need.
for example:
pi is an irrational number.
it is represented in the calculator by 3.141592654.....
how far out the accuracy is recorded in the calculator is not known but it probably goes out about 15 digits.
you want to know the circumference of a circle and the accuracy you require is 3 decimal places.
no problem because the accuracy of pi goes out 15 decimal places so you will have no problem getting your answer even though pi is an irrational number.
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