863
Irrational numbers are infinitely dense. That is to say, between any two irrational (or rational) numbers there is an infinite number of irrational numbers. So, for any irrational number close to 6 it is always possible to find another that is closer; and then another that is even closer; and then another that is even closer that that, ...
See lemma 1.2 from the cut-the-knot link. Yes, you can.
the numbers between 0 and 1 is 0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,0.10.
0.12=1.1201001000100001 0.13=1.12101001000100001
It is proven that between two irrational numbers there's an irrational number. There's no method, you just know you can find the number.
Find the difference between the two numbers, then add an irrational number between zero and one, divided by this difference, to the lower number. Such an irrational number might be pi/10, (square root of 2) / 2, etc.
863
I can't tell you the irrational number between 0.2 and 0.3; there an infinite number of irrationals in this range.For an example - root(2) / 7 is slightly more than 0.202, and is irrational.
Any number that can't be expessed as a fraction is an irrational number as for example the square root of 4.5
There may be many easier and better ways, but here's how I would do it: -- Square the first given irrational number. -- Square the second irrational number. -- Pick a nice ugly complicated decimal between the two squares. -- Take the square root of the number you picked. It's definitely between the two given numbers, and it would be a miracle if it's not irrational.
Any number that can't be expressed as a fraction is irrational
sqrt(5) and sqrt(6)
There are an infinite number of integers that meet this criteria.Ans 2Root 2 and root 3 are both irrational, but there is no integer between them.Did you mean to say 'an infinite number of pairs of integers" ?
Sqrt(27.05) is one such number. Its decimal approximation, to the nearest hundredth, is 5.20 - but to the nearest thousandth is is 5.201
An Irrational Number is a real number that cannotbe written as a simple fraction.
Irrational numbers are infinitely dense. That is to say, between any two irrational (or rational) numbers there is an infinite number of irrational numbers. So, for any irrational number close to 6 it is always possible to find another that is closer; and then another that is even closer; and then another that is even closer that that, ...