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Determine if 0.515115111511115111115...0.515115111511115111115... is rational or irrational and give a reason for your answer?
Mariam Dini
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Can you add two irrational numbers to get a rational number?
Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.
What is the 15.125 it is a rational or irrational in math?
It is a rational number. The reason that it is rational is that you can represent it as a fraction, where the denominator (the number at the bottom of the fraction) is not equal to 0.So, for example, as we could write the number 15.125 as 15125/1000 then it is rational.
How do you estimate an irrational number and why do you need for?
How an irrational number is estimated depends on the nature of the number. The reason for estimating them is that two of the most important numbers in mathematics: pi in geometry and e in calculus, are both irrational. Also, the diagonal of a unit square is of length sqrt(2), an irrational. Irrational numbers crop up everywhere: there are more irrational numbers than there are rational.
Are there more rational than irrational numbers?
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.
Why did the roman empire Caligula fall?
Caligula "fell" because he was assassinated. The reason for his murder were because of his irrational actions.Caligula "fell" because he was assassinated. The reason for his murder were because of his irrational actions.Caligula "fell" because he was assassinated. The reason for his murder were because of his irrational actions.Caligula "fell" because he was assassinated. The reason for his murder were because of his irrational actions.Caligula "fell" because he was assassinated. The reason for his murder were because of his irrational actions.Caligula "fell" because he was assassinated. The reason for his murder were because of his irrational actions.Caligula "fell" because he was assassinated. The reason for his murder were because of his irrational actions.Caligula "fell" because he was assassinated. The reason for his murder were because of his irrational actions.Caligula "fell" because he was assassinated. The reason for his murder were because of his irrational actions.
Is 7329 rational or irrational an give a reason why?
7329 is an integer. All integers are rational.Proof : 7329/1 is a ratio of two integers; it is equal to 7329.n/1 is a ratio, and equal to n.
Man as rational organism?
In order to hypothesize, declare, disprove, argue against etc. the "irrational" behavior(s) of an organism we are first required to determine the definition of "rational" and "rationale". One of the significant "problems" with declaring man as being "irrational" is that we are seeking/sharing information associated with this very topic. In order to acknowledge the existence of the potential for irrational behavior, not to mention rational behavior, some form of rationale is required. In either of these behaviors (e.g. seeking or sharing) each of us have exhibited several examples of reason, principle and even accounting (not the financial science). However, one of the significant issues, with declaring man as being a rational organism, rests within the concept of rationalization. In order to "use" rationale, the presence of some form of emotion or emotional behavior is required to exist or to be in question (e.g. yeah but, with that, what about, no I, etc.). Within this process, the "individual" in question is seeking to support an explanation for which no "prime reason" can be provided. In this, man is required to apply some form of unconscious (e.g. irrational) information to complete a cycle (e.g. answer a question, solve a puzzle, eliminate confusion to the greatest extent possible etc.). With that, "rational processes" are no longer the only process associated with "thought".
Is 3 pi irrational?
Pi, is an irrational number (it cannot be written as a fraction) For this reason, 3 times pi is also irrational.
How would you put rational in a sentence?
Rational means to be reasonable or to have reason. Let us be reasonable/rational. He was rational in his desition.
Why was an irrational number called a 'surd' as opposed to an 'irrat'?
The term surd traces back to al-Khwārizmī, who referred to rational and irrational numbers as audible and inaudible, respectively. This later led to the Arabic word "أصم‎" (asamm, meaning "deaf" or "dumb") for irrational number being translated into Latin as "surdus" (meaning "deaf" or "mute").
What are the reasons for phobia of maths?
Phobias do not have a reason they are irrational fears.
What is irrational exuberance?
Extreme happiness and excitement for no apparent reason.
