Question

what do you do to check whether a number is rational or irrational. In your explanation use an example of an irrational and rational number.

Answer 1

A rational number is a number that can be represented as a ratio of two other numbers, or as a fraction of two integers. I guess the question is what number you're trying to do this to.

Answer 2

So if you're given a number, you can try and figure out whether it's rational or irrational just by the way its presented.

Answer 3

for example, a number given as 2 or 5 or -26 is clearly rational, but then so is: 2.333... especially if one has a line over the 3's.

Answer 4

Irrational Numbers

An Irrational Number is a real number that cannot be written as a simple fraction.

Irrational means not Rational

Examples:



Rational Numbers

OK. A Rational Number can be written as a Ratio of two integers (ie a simple fraction).

Example: 1.5 is rational, because it can be written as the ratio 3/2

Example: 7 is rational, because it can be written as the ratio 7/1

Example 0.333... (3 repeating) is also rational, because it can be written as the ratio 1/3



Irrational Numbers

But some numbers cannot be written as a ratio of two integers ...

...they are called Irrational Numbers.

Answer 5

Because if the fraction continues forever, you can manipulate things to make it come out that way. For example with 2.33333... 1/3 is 3.33333, and 2 is 6/3. Thus 2.33333... will be\[\frac{ 1 }{ 3 } + \frac{ 6 }{ 3 } = \frac{ 7 }{ 3 } = 2.33333...\]

Answer 6

So you can tell if it is Rational or Irrational by trying to write the number as a simple fraction.

Example: 9.5 can be written as a simple fraction like this:

9.5 = 19/2

So it is a rational number (and so is not irrational)

Answer 7

ON the other hand, if you're given a number like \[\sqrt{2}\] or something, it'll probably be irrational, though it might not be, as in the case of \[\sqrt{4} = 2\]

Answer 8

Rational numbers and irrational numbers are subsets of the real numbers. You can't have a number that is rational or irrational but not a real number. Unless there's a number system that's similarly classified in such a way.

Answer 9

I guess what I'm saying is that if you're given a number, the way it's written down will serve as an indication, and if you can manipulate the number into a fraction then it must be rational. I can't off the top of my head think of a method of finding out if a variable x stands for a rational or irrational number other than by context.