How do i write an irrational number algebraically if a rational number is a/b?

Answer 1

the whole point of an irrational number is that it cant be expressed as a quotient of two integers.

Try (A+(B/C)/D

Answer 2

There's no general way. Many of the irrational numbers you will use will be expressible in terms of radicals (square roots, cube roots etc.) and rational numbers (e.g. 3 + √2). However, some numbers, like π and e, are basically not expressible in terms of any other simpler numbers.

Also note that two formulations suggested above (A/(B/C)/D and a/(a-b)) will not give you irrational numbers unless at least one of the component numbers is itself irrational. Any product, quotient, sum or difference of rational numbers is rational.

The answerer who said that a/(a-b) would give you an irrational number completely misunderstood the section of the Wikipedia article on irrational numbers to which they linked, which is a proof that (1 + √5)/2 is irrational.

Answer 3

If the ellipse (...) follows the variety, that could be a sturdy wager that the variety is irrational or repeating which generally additionally has a bar over the repeating sections. maximum repeating numbers have a rational representation. If there are actually not any ellipses on the tip of the variety, take it at face fee. It turns into rational. keep in mind: An irrational variety is a variety that cannot be expressed as a fragment

Answer 4

First we have 2 types of irrational numbers:

1- those you can turn into a rational (recurring)
2- those never ending you can do nothing about-( eg. pi =3.142857......goes on for ever).
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Worked out example of a 'recuring'irrational number .

Question: express 0.424242424... as a fraction.

Answer: 14/33
How?

This is the method:
0.424242424...is a 'recurring' irrational, where the recurring part is 4 and 2.(hence we can write it as a fraction).

let r=0.42
multiply both sides of equation by 100:

100r=42.4242424...

subtract r (from both sides):
100r(-r)=42.4242424...(-0.42)=
99r=42

so r=42/99

42 can be divided by 3 giving 14
99can be divided by 3 giving 33

hence r becomes: r=42/99=14/33

and your most simplified answer for 0.424242424...=14/33 (in a fraction form)

NB. when the recurring part contains:
2 digits use 100
3 digits use 1000
1 digit use 10
etc...

I hope that helps ....Good luck :)

Answer 5

sorry cant be done as rational means in the form a/b and a/b is always defined as a rational.
irrational numbers cannot be written ( text book)
as algebric expressions dats why they are called irrationals or those that arent rational.
youll have to write them as irrational.
for our convienence they are simplified
for eg.
Pi is irrational for our convinience it is written as 22/7 or 3.14

Answer 6

It depends on what your irrational number is.

For example:

The irrational no 3.1416... is written as the greek letter pi.

The square root of three is written like 3 is under a radical sign.

There many irrational numbers. We could not name them all!

Answer 7

Instead of a and b i use the variables i and e for more clear example.
e=2.718281828459015.............(a rational number)
E =(Sigma) SUMMATION
! = Factorial function
i= set of all whole numbers from 0 to infinity.


. . infinity
e= E (1 / i! ) . . . . . .(an algebric equation)
. . i=0

Description:
e= sumation of reciprocal of factorials of all whole rational numbers from 0 to infinity.

In this way we can represent many irrational numbers in a sum of series which infact will be an algebric equation.

Answer 8

irrational numbers cannot be put into algebretic form like a/b at all. that is the whole point of it....if you could, do you think pi would be said as 3.147..........yada yada yada? or as a simple fraction....

Answer 9

if a/b is rational then b/a is irrational