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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
Why is 4.323223222 an irrational number if you can predict what comes next?
Being rational or irrational is not about "predicting the next digit"; the definition of a rational number is that you can write it as a fraction, with integer numerator and denominator.
Being rational or irrational is not about "predicting the next digit"; the definition of a rational number is that you can write it as a fraction, with integer numerator and denominator.
Being rational or irrational is not about "predicting the next digit"; the definition of a rational number is that you can write it as a fraction, with integer numerator and denominator.
Being rational or irrational is not about "predicting the next digit"; the definition of a rational number is that you can write it as a fraction, with integer numerator and denominator.
Find a rational number between two irrational numbers?
There are an infinite number of integers that meet this criteria.
Ans 2
Root 2 and root 3 are both irrational, but there is no integer between them.
Did you mean to say 'an infinite number of pairs of integers" ?
How do you figure out if a number is rational or irrational?
If the number can be expressed in the form a/b where a and b are both integers and b ≠ 0, then it is proved rational.
If you want to prove that it is irrational, then there are many complicated and different steps depending on the type of irrational number. (Yes there are different types)
-2 is rational. It can be expressed as a ratio/fraction of 2 integers (can be negative or positive), and -2 = -2/1 or -4/2.
If three different irrational numbers are multiplied is the result an irrational number?
Not necessarily. The cube roots of 4, 6 and 9 are all irrational (and different). But their product is 6, not just rational, but an integer.
Is 0.712 repeating a rational number is a irrational?
0.712 repeating is a rational number because it can be expressed as a fraction in the form of 712/999
Is non-terminating decimal is a rational or irrational number?
Either.
If it is non-terminating but recurrent (after some point) it is rational. If it is non-terminating AND non-recurrent then it is irrational.
-22 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Yes because 0.164 can be expressed as a fraction in the form of 41/250
Is the square root of thirteen an integer rational number irrational number or whole number?
irrational
Is the quotient of two irrational numbers is irrational?
In general, no. It is possible though. (2pi)/pi is rational. pi2/pi is irrational. The ratio of two rationals numbers is always rational and the ratio of a rational and an irrational is always irrational.
Is 3.8 irrational or rational?
3.8 is a rational number because it can be expressed as a fraction in the form of 19/5
No. It is a whole number and it can be written as a fraction, so it is not irrational.
How can you find irrational number between any two number?
There are infinitely many irrational numbers between any two numbers - rational or irrational.
Suppose x and y are two irrational numbers.
Consider x2 and y2. Is there any integer between them that is not a perfect square? If so, the square root of that number is an irrational between x and y.
If not, consider x3 and y3 and look for an integer between them that is not a perfect cube. If there is then the cube root of that number will meet your requirements.
If not, try x4 and y4 and then x5 and y5 etc. In a school exercise you are extremely unlikely to have to go as far as the cubes!
If a number is irrational then is it a natural number?
Many "natural" numbers are irrational - meaning, they cannot be expressed as a ratio or fraction. Pi, the ratio of the circumference of a circle to the diameter, cannot be expressed as a fraction, and is APPROXIMATELY equal to 3.14.
The number "e" is approximately equal to 2.718.
How do you know whether a number is non-terminating repeating?
A non-terminating repeating number must be rational. When its fractional part is in its simplest form, the denominator must have a prime factor other than 2 or 5.
Is the square root of 225 a subset of the irrational numbers?
The square root of 225 is 15, which is NOT an irrational number.
