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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 15.2 a rationtal number or irrational number?
RATIONAL.
Any DEcimal Number that can be made into a fraction/ratio is RATIONAL.
So 0.3333..... is Rational as its fraction is '1/3'
BUT
pi = 3.141592.... is IRRATIONAL because in casual terms the decimal digits are NOT in any regular order.
As a rough rule, All numbers are rational except. ;-
pi , 'e' and the square roots of prime numbers.
NB There are other Irrational numbers too!!!!!
What is 9.23 Rational or irrational number?
The number 9.23 is a rational number. A rational number is any number that can be expressed as a fraction of two integers, where the denominator is not zero. In this case, 9.23 can be written as 923/100, which is a fraction of two integers, making it a rational number.
Is -4.7 rational or irrational?
-4.7 is the ratio of -47 to 100. That's rational.
The answer to every question like this is always 'rational', because any number
that you can completely write down on paper with digits is a rational number.
Oh honey, 68 is as rational as it gets. It's a whole number, which means it can be expressed as a ratio of two integers. So, no need to lose sleep over this one - 68 is as rational as a sensible pair of shoes.
Is the square root of 97 rational or irrational?
The square root of 97 is an irrational number. This is because the square root of 97 cannot be expressed as a fraction of two integers. In other words, the decimal representation of the square root of 97 goes on forever without repeating, making it an irrational number.
Which number is irrational -5.72?
There are no irrational numbers in the value -5.72. All of the components of the value are represented by rational numbers.
An irrational number is any number that cannot be represented by a fraction a/b where a and b are integers.
-5.72 itself is rational as it can be represented by -572 / 100.
The digits of the value are also rational as they can be represented as -5/1, 7/1 and 2/1, respectively.
Well, let's take a moment to appreciate the beauty of numbers. In this case, -4.9 is not an irrational number because it can be expressed as a fraction -49/10. Remember, every number has its own unique charm, whether it's rational or irrational. Just embrace the numbers and let them bring joy to your mathematical world.
Is the square root of negative 121 rational irrational or a real number?
The square root of -121 is imaginary. It has value of i11.
It is not rational, irrational, nor real. The coefficient of i, 11, is real and rational, but the result of multiplying i by 11 is imaginary.
Now, The Coefficient of (i11) is a complex number, because when dealing with i, the true form is the square root of -1, and so this also means that you still have 2 answers, positive and negative i11, and so the square root of -121 is imaginary, or complex rational number. But, because it is complex, it is not truly rational, all this means is that you end up with aninteger in your complex answer. So, To answer your question, the answer is non of the above, just imaginary. and the value is plus or minus (i11).
NO!!!!
Because it can be converted to a RATIO/FRACTION.
14.142 = 14 142/1000 = 14 71/500
NB Irrational numbers are those were the decimals recurr to infinity AND there is no regular order in the decimal digits.
'pi' is probably the most well known irrational number.
pi = 3.141592....
NB When given pi = 3.14 in school , this is only an approximation.
Othe irrational numbers are the 'square roots of prime numbers'.
sqrt(2) = 1.414213562....
sqrt(3) = 1.7320508...
sqrt(5) = 2.236067978....
et.seq.
Is -2.75 an irrational or rational number?
It is rational. An irrational number is a number that you cannot define by a fraction or a decimal. Since you wrote it as a decimal, it is rational. The fact that it is negative does not matter.
Is the square root of -255 rational or irrational?
Irrational (and a multiple of i), as the square root of 255 is irrational.
Is 306 rational or irrational?
RATIONAL.
Irrational numbers are those that have decimals going to infinity AND the decimal digits are NOT in any regular order.
pi = 3.141592.... is the most well known irrational number.
Others being the square roots of prime numbers.
Is 0.314 rational or irrational?
0.314 is rational. However, if you are refering to pi (which is 3.14159265...) then it would be irrational because it continues on forevor with no pattern.
Is 0.6666 an irrational number?
NO!!!
As given it is a terminating decimal, and as a fraction it is 6666/10000
However,as a recurring decimal to infinity, it can be converted to a ratio/fraction .
Hence
Let P = 0.66666....
10P = 6.66666....
Subtract
9P = 6.0 (Note the recurring decimal subtract to 'zero'.
Hence
9P = 6
P = 6/9
Cancel down by '3'
P = 2/3
NB Resurring decimals to infinity are written as 0.666... ( Note the three or more dots. This indicates to mathematicians, that it recurs to infinity, otherwise it is a terminating decimal.
NNB Irrational numbers are those that recur to inifinity AND the decimal digits are not in any regular order. . 'pi' 3.141592.... being the most well known irrational number.
Every irrational number can be expressed as a quotient of integers?
WRONG!!!!!
Irrational numbers CANNOT be expressed as a quotient(fraction).
Casually, irrational numbers are those were the decimals go to infinity AND there is no regular order in the decimal digits.
e.g.
pi = 3.1415192.... is Irrational
3.3333.... is rational.
NO!!! Because 1.325 is a terminating decimal.
Casually, irrational numbers have the decimals digits to infinity, and there is no regular order in the digital sequence.
More correctly , an irrational number CANNOT be converted into a Rational Number /Quotient/ Fraction.
NB pi = 3.141592.... is probably the most well known irrational number.
Is every irrational number also real?
Yes, every irrational number is also a real number.
Real numbers include all the numbers on the number line, which consists of both rational and irrational numbers. Rational numbers can be expressed as fractions, whereas irrational numbers cannot be expressed as simple fractions.
So, while all irrational numbers are real numbers, not all real numbers are irrational—some are rational.
NO!!!!
Any terminating decimal is NOT irrational.
'3.3' is a terminating decimal.
NB An IRRATIONAL number is one in which the decimals go to infinity AND the digits are not in any regular order.
'pi' is the most well known irrational number.
pi =~= 3.141592....
0.6 is NOT irrational
However, pi = 3.141592.... is Irrational.
When miultiplied together , the answer is IRRATIONAL
0.6 X 3.141592.... = 1.884955592....
