Find an irrational numbers between 4/9 and 5/9.

Question

photon336 · Answer

I guess we would have to find a decimal with a number that doesn't repeat, or terminate.

daniel.ohearn1 · Answer

Is it find a irrational number or all irrational numbers between those fractions?

jim_thompson5910 · Answer

It's impossible to list out all of the irrational numbers between any two real numbers

mathisfun13 · Answer

.4510100100010000.. is one

mathisfun13 · Answer

because it is greater than .4444... and less than .5555...

jim_thompson5910 · Answer

correct @mathisfun13

mathisfun13 · Answer

I just need another example

jim_thompson5910 · Answer

another one is 

step 1) take the midpoint of 0.4444... and 0.5555....
midpoint formula is M = (a+b)/2

step 2) add on some very small irrational number, like pi/1000 to make the overall result irrational

jim_thompson5910 · Answer

or you can compute the geometric mean of 4/9 and 5/9

across · Answer

gee... this cannot be easier...$$\frac{16}{81}<\frac{21}{81}<\frac{25}{81}\\frac{4}{9}<\frac{\sqrt{21}}{9}<\frac{5}{9}$$

jim_thompson5910 · Answer

that works too