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rational vs. irrational numbers











































I am reading a text book and it says that in the equations to change degrees Fahrenheit to degrees Celsius and in the opposite equation:

F = (9/5)(C)+32

C = (5/9)(F-32)

that 9/5 is a rational number and 5/9 is an irrational number.

I don't understand because the definition of rational numbers is numbers that have the form a/b.

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Oct 27, 2010
Rational vs. Irrational Numbers
by: Staff



The question:


I am reading a text book and it says that in the equations to change degrees Fahrenheit to degrees Celsius and in the opposite equation:

F = (9/5)(C)+32

C = (5/9)(F-32)

that 9/5 is a rational number and 5/9 is an irrational number.

I don't understand because the definition of rational numbers is numbers that have the form a/b.




The answer:

Let’s start with your definition of a rational number:

A rational number is a number which can be written as a fraction a/b.

You are correct.

Have you ever noticed that the first 5 letters of the word rational spell the word RATIO. We use ratios in everyday life all the time. For example, one person might say a car gets 25 miles per gallon. This is the ratio 25:1, or the fraction 25/1. Another person might say that to mix cookie batter add 1 cup of water for every 3 cups of flour. This is the ratio 1:3, or the fraction 1/3.

Both of your numbers (9/5 and 5/9) are rational numbers because they can be written as a fraction.

What is probably bothering you is the number 5/9 = 0.5555555…

The decimal equivalent of 5/9 is a repeating decimal, but it is still a rational number. The pattern .5555… repeats itself.


An IRRATIONAL NUMBER, on the other hand cannot be written as a fraction. The decimal value of an irrational number does not have a pattern which repeats itself.


An example of an irrational number is the square root of 2.

The square root of 2 = 1. 4142135623 7309504880 1688724209 6980785696 7187537694 8073176679 7379907324 7846210703 8850387534 3276415727 3501384623 and so on. The numbers do not appear in a pattern which repeats itself, no matter how many decimal places are computed.


One way to remember the difference between the decimal equivalent of a rational number and the decimal equivalent of an irrational number is:

The decimal equivalent of a rational number will terminate, or have a repeating pattern.

The decimal equivalent of an irrational number will never terminate, and it never has a repeating pattern. This is sort of like an irrational person: there is NO PATTERN to their behavior – what they say or do is totally off the wall.






Thanks for writing.


Staff
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