what are rational and irrational numbers on a number line?

Question

how can it be sketched on a number line

Answer 1

One of the fun parts of advanced math.

The rational numbers and the irrational numbers are infinitely dense. That is, between any two numbers I can find an infinite number of rationals and irrationals.

But, the rationals are countable. That means that they can be put into a 1 to 1 correspondence with the whole numbers. Irrationals cannot.

Oh, rational numbers can be expressed as the ratio of two whole numbers, like 1/3. Irrationals cannot. The square root of any prime number is irrational. That was proved a couple thousand years ago. Every graduate math student has to do it too! It's really a pretty simple proof.

Hopefully this helped.

Answer 2

If you considered the set of irrational numbers a forming a number line, yes the integers and all the rational numbers would be holes. this is not a standard way to look at things but there is nothing wrong with it at all. However, the irrational line with holes at the rationals is a very different kind of mathematical object from the rational line with holes at the irrationals. They are not two symmetric ways of looking at things, so to speak. (Which set we call rational and which we call irrational is not arbitrary.) for example, I can add two irrational numbers on the irrational number line and get a sum which is "off" the line. (the sum can be rational....a hole). but if I add two numbers on the rational number line, the sum is always on the rational number line(I don't hit a hole)

Answer 3

They are just what they sound like. Rational numbers can be expressed as the ratio of two integers ( i.e. a / b). Irrational numbers cannot. The numbers pi (the ratio of the circumference divided by the diameter of a circle) and e (the base of the natural logarithms) are non-terminating, non-repeating numbers whose decimal values have been calculated out to millions of places with no apparent pattern of repetition. Thus they are irrational numbers because no two integers have yet been discovered which give their precise values.

Answer 4

For definitions, go to wikipedia. For examples, -1, 0, 1, 2, 3 are all rational; pi and e are irrational.

Answer 5

irrational numbers are ones that can not be shown as a fraction.
Pi. e, the sqr root of 2.