how can we express irrational numbers into fractions ?

Question

tell us also about the continued fraction expansion .

Answer 1

As others have indicated, an irrational number cannot, by definition, be expressed as a fraction (or “ratio,” thus “irrational” or “not rational”).

But I think you’re asking about infinite series here. For example, pi is irrational, but it can be expressed as an infinite sum of fractions: pi/4=1-1/3+1/5-1/7+1/9-... Where the ellipses indicates that one should continue the pattern of alternating addition and subtraction of the inverse of increasing odd numbers.

The transcendental numbers pi and e can be expressed as infinite series because they are related to differentiable mathematical functions. Using a Taylor series, one can evaluate a function at a certain point, resulting in a value for pi or e, as examples.

Another example of an irrational number that can be expressed as an infinite series is the Golden Ratio phi, for much stranger reasons.

Not every irrational number can be expressed in this way, however. In fact, the vast majority of irrational numbers cannot be expressed as any kind of infinite series.

Answer 2

Irrational numbers are not expressable as "A divided by B where both A and B are integers." All other real numbers (as opposed to imaginary numbers or complex numbers) CAN be expressed as "A divided by B where both A and B are integers."
This forms a RATIO; thus Irrational numbers can't by definition be expressed as a ratio of two other rational numbers.
Take the ratio of the circumference of a circle ("c") to its radius ("r"). If "r" is known and a rational number, then "c" MUST be irrational and vice versa.

Answer 3

irrational number is one which cannot be expressed as a fraction

Answer 4

Irrational Numbers can be a decimal but not a fraction.

to the right of the decimal point, a irrational number has endless non-repeating digits

Example

π =3.141592654. . .

Answer 5

as others have said, you can't express irrational numbers as fractions, by definition.

For help with continued fractions see for instance http://mathworld.wolfram.com/ContinuedFraction.html or http://en.wikipedia.org/wiki/Continued_fraction

Answer 6

you can express irrational nos only as approx fractions like pi (22/7)
i think you mean repeating decimals like
1.121212121212.......
heres how you do thay
x=1.121212121212.........
100x=112.1212121212....
100x-x=112.121212.....-1.121212......
99x=111
x=111/99

Answer 7

Some yes, some no (that's why they're irrational)

Answer 8

I don't know

Answer 9

i cant explain it