# 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.

### Comments for rational vs. irrational numbers

 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 www.solving-math-problems.com

 Sep 13, 2018 rational NEW by: princess 0.55555.... 3.14 9.2 7.2222... 2/5 40/7 43/21 -15/3 -0.898989.. 1 2/3 -211.211