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Irrational Numbers
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. While their existence was once kept secret from the public for philosophical reasons, they are now well accepted, yet still surprisingly hard to prove on an individual basis. Please post all questions about irrational numbers, including the famous examples of π, e, and √2, into this category.
3,962 Questions
What is a infinite rational numbers?
There is no infinite rational number. There are infinitely many of them but that is not the same.
Is -130 rational or irrational?
130 is a rational number.
A "rational" number is any number than can be expressed as a fraction or "ratio". 130 is a rational number because it can be expressed as a fraction, such as 130/1.
No. An irrational number is not expressible as a ratio of two integers. An irrational number has infinite and nonrecurring expansion. An example is pi, or the square root of 2.
Why is the square root of 200 irrational?
because the square root of 200 has a decimal that doesn't end or repeat.
like pi 3.141592654........ no repetition/pattern and it goes on forever so it is irrational
no
No; a mixed number is rational. Irrational means it cannot be written as a fraction, but mixed numbers can always be written as (improper) fractions.
*By the way, improper fractions are still fractions, despite their degrading name! It just means the fraction's numerator is larger than its denominator.
Is the square root of 8 over 25 rational irrational or a real number?
The square root of 8 over 25 is irrational, and real.
Why is the sum of two irrational numbers not always irrational?
Because the irrational parts may cancel out.
For example, 1 + sqrt(2) and 5 - sqrt(2) are both irrational but their sum is 1 + 5 = 6.
What is the answer of g is an irrational number between 2 and 4?
The square root of 3 is an irrational number
Is the square root of 133 irrational or rational explain?
It is irrational.
133 = 7*17 and so is not the square of any rational number. Therefore its square root cannot be rational.
No.
An irrational number cannot be expressed as the quotient of two integers.
35.6 = 356/10 and both 356 and 10 are integers.
Hint: A terminating decimal is never irrational.
Are most numbers rational or irrational?
The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible.
All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.
Is -155.2333333333 an irrational number?
No.
It is rational as it can be written as one integer divided by another, i.e.
-1,552,333,333,333/10,000,000,000
How do you prove by contradiction that square root of 7 is an irrational number?
If √7 is rational, then it can be expressed by some number a/b (in lowest terms). This would mean: (a/b)² = 7. Squaring, a² / b² = 7. Multiplying by b², a² = 7b². If a and b are in lowest terms (as supposed), their squares would each have an even number of prime factors. 7b² has one more prime factor than b², meaning it would have an odd number of prime factors. Every composite has a unique prime factorization and can't have both an even and odd number of prime factors. This contradiction forces the supposition wrong, so √7 cannot be rational. It is therefore irrational.
Can irrational numbers cannot be represented by points on the real number line?
These number can also be represented on real line.
Integers (whole numbers) are RATIONAL.
Why?
Well,
a real number a is irrational if and only it cannot be written in lowest reducible form p/q in which p is an integer( - 10000, - 5, 0,1, 32, 34, etc.), and q is a natural number(1, 2, 3, 4, 5, etc.) and they share no common factor besides 1, that's is
there is no number b that is not 1 such that both p and q divides b.
34 is an integer, and we know for any number a
a = 1 x a and 1 = 1 / 1
so
a = 1 x a
a = 1 / 1 x a
a = a / 1
So 34 = 34 / 1.
Now, we have an integer (34) as p, and a natural number (1) as q.
Now you know if it's a rational number or not?
