because the # line shows the rational #'s in order from least to greatest
how do u put rational numbers in order from lest to greatest
order the numbers from least to greatest
To order fractions and decimals, you can either write them all in the same form and then compare them, or place them on a number line. Recall that numbers increase in value as you move from left to right along a number line.
The answer requires a bit of mathematics, but goes like this:The product of any 2 rational numbers is a rational number.The product of any 2 irrational number is an irrational number.The product of a rational and an irrational number is an irrational number!Therefore simple logic tells us that there are more irrational numbers than rational numbers. There is a way to structure this mathematically, and I believe it is called an "Inductive Proof".Interesting !I'm going to say "No".I reason thusly:-- For every rational number 'N', you can multiply or divide it by 'e', add it to 'e',or subtract it from 'e', and the result is irrational.-- You can multiply or divide it by (pi), add it to (pi), or subtract it from (pi),and the result is irrational.-- You can take its square root, and more times than not, its square root is irrational.There may be others that didn't occur to me just now. But even if there aren't,here are a bunch of irrational numbers that you can make from every rational one.This leads me to believe that there are more irrational numbers than rational ones.-------------------------------------------------------------------------------------------------------There are infinitely many more irrationals than rationals; this was proved by G. Cantor (born 1845, died 1918). His proof is basically:The rational numbers can be listed by assigning to each of the counting numbers (1, 2, 3,...) one of the rational numbers in such a way that every rational number is assigned to at least one counting number;If it is assumed that every irrational number can be assigned to at least one counting numbers (like the rationals), then with such a list it is possible to find an irrational number that is not on the list; so is it not possible as there are more irrationals than there are counting numbers, which has shown to be the same size as the rational numbers, thus showing that there are more irrationals than rationals.
because the # line shows the rational #'s in order from least to greatest
how do u put rational numbers in order from lest to greatest
first finding the whole number and then sort them out from least to greatest in answers
If the pattern continues, with one more zero in each group, then it is IRRATIONAL. For a number to be rational, EXACTLY THE SAME pattern must repeat over and over, at least after a certain point.
Any subset of rational numbers can be ordered.
Any subset of rational numbers.
At least one of the factors has to be irrational.* An irrational number times ANY number (except zero) is irrational. * The product of two irrational numbers can be either rational or irrational.
you have to compare the common fractions
you put the least one first then the most fraction last
If the numbers are irrational, then yes. If the numbers are rational, no. If they are rational, they can be modelled as a and b, in which case the number ab would be a multiple of both. If there is at least one common multiple, then there must be a lowest common multiple.
order the numbers from least to greatest
Convert them to decimals and order them least to greatest.