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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
Is 0.09 a rational or irrational number?
0.09 is a rational number because it can be expressed as a fraction, specifically 9/100. Rational numbers are defined as numbers that can be written as the quotient of two integers, and since 0.09 fits this definition, it is classified as rational.
Is 5.56776436283 an irrational number?
Yes, 5.56776436283 is an irrational number. An irrational number cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion. Since the decimal representation provided appears to be a non-repeating decimal, it indicates that the number is irrational.
No, 8.9745 is not an irrational number; it is a rational number because it can be expressed as a fraction. Specifically, it can be written as 89745/10000, which is the ratio of two integers. Rational numbers are those that can be represented as the quotient of two integers, and 8.9745 fits that definition.
Is 1.4141414141 irrational or rational?
The number 1.4141414141 is a rational number because it can be expressed as a fraction of two integers. Specifically, it can be represented as 141414141/100000000, which is a finite decimal. In contrast, the square root of 2, which is approximately 1.41421356..., is an example of an irrational number.
Is 2.343443444 rational or irrational?
The number 2.343443444 is a rational number because it can be expressed as a fraction. Specifically, it can be written as ( \frac{2343443444}{1000000000} ). Since it has a finite decimal representation, it qualifies as rational.
Is the square root of 16 a rational or an irrational number?
sqrt(16) = +/- 3
Both +4 & -4 are rational.
NB The square roots of prime numbers are irrational
e.g. sqrt(2) = 1.413213562....
sqrt(3) = 1.732050808....
sqrt(5) = 2.236067978....
et seq.,
Is 1.67 rational or irrational?
Oh honey, 1.67 is as rational as a well-organized sock drawer. It's a decimal number that can be expressed as a fraction, so it falls into the rational number club. No need to overcomplicate things, darling.
Are negative square roots rational or irrational?
Oh, dude, negative square roots are actually considered irrational numbers. I know, right? It's like, they're not rational because they can't be expressed as a simple fraction. So yeah, negative square roots are definitely in the irrational club. Cool, right?
Is 7 over 8 a rational number or irrational number?
7 over 8, which can be written as 7/8, is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers, and the denominator is not zero. Since 7 and 8 are both integers, and 8 is not zero, 7/8 is a rational number.
No it is not a rational number,similar like 22/7 which is also a irrational number,becoz they are not totally divisible.
Which set is the intersection of integers and rational numbers?
The intersection of integers and rational numbers is the set of integers. Integers are whole numbers that can be positive, negative, or zero, while rational numbers are numbers that can be expressed as a ratio of two integers. Since all integers can be expressed as a ratio of the integer itself and 1, they are a subset of rational numbers, making their intersection the set of integers.
Is -3.72 rational or irrational?
-3.72 is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. In the case of -3.72, it can be written as -372/100, which is a fraction where both the numerator and denominator are integers. Therefore, -3.72 is a rational number.
What is an irrational number between 2 and 4?
Ah, what a happy little question. An example of an irrational number between 2 and 4 is the square root of 3, which is approximately 1.732. It's like a little mystery hiding between our familiar whole numbers, adding a touch of magic to our mathematical landscape. Just remember, there are infinite possibilities in the world of numbers, waiting for us to explore and appreciate.
What is a irrational number between 6 and 7?
Oh honey, let me tell you, pi is an irrational number that falls between 6 and 7. It's approximately 3.14159, but it goes on forever without repeating. So, if you're looking for a number that's a little bit wild and unpredictable, pi is your go-to gal.
NO because it can be converted to a ratiop/fraction 31.6 = 31 6/10 = 31 3/5 .
NB Irrational numbers are those that go to infinity AND there is NO reguklar order in the digits.
pi = 3.141592.... Is the most well known irrational number.
but
3.141414... is NOT irrational, because the decimals are in a regular order of 'one' , 'four' .
What is the square root of pi?
The square root of the square root of the square root of something is called the 8th root. The 8th root of pi is approximately 1.15383506784999.
Is -14 a rational or irrational number?
14 is rational. Rational numbers are numbers that can be written as a fraction. Irrational Numbers cannot be expressed as a fraction.
No. If you write an irrational number as a decimal, it will have an infinite number of decimal digits that don't repeat periodically.
Is 3.45 a rational or irrational number?
Well, honey, let me break it down for you. 3.45 is a rational number because it can be expressed as a simple fraction, 345/100. So, yes, it's rational, unlike some of the decisions I've seen people make in my 99 years on this planet.
What are all of the perfect square numbers from 1-500?
Oh, what a delightful question! Perfect square numbers are like little treasures in the world of math. From 1 to 500, you will find perfect squares like 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484. Each one is unique and beautiful in its own way.
Why an irrational number plus an irrational number equal a rational?
Well, darling, when you add two irrational numbers together, they can sometimes magically cancel each other out in such a way that the sum ends up being a rational number. It's like mixing oil and water and somehow getting a delicious vinaigrette. Math can be a wild ride, honey.
NO!!! 5.1 is RATIONAL , because the ',1' moiety can be converted to a quotient(fraction).
IRRATIONAL numbers are those were the decimals go to infinity AND the decimal digits are not in any regular order. More formally the decimal cannot be converted into a RATIO/QUOTIENT/FRACTION/
You are probably given 'pi ' = 3.14 in school . However 'pi' is irrational because the number is 3.141592654.... (The dots indicate mathemtically that it goes to infinity.
Supa-Dupa computers have calculated 'pi' to 50 billion places are still going.
Other irrational numbers are 'sqrt(2) = 1.414213562....
sqrt(3) = 1.7320508....
etc.,
The square roots of Prime Numbers are Irrational.
However. something like 4.333333.... is NOT irrational nor 43.434343.... be cause it can be converted into a fraction. By the above statement the decimals are in a regular order.
So treat all numbers are RATIONAL, except those by the above rule.
