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Why is the productof a non zero rational number and an irrational number is irrational?
Let A be a non-zero rational number and B be an irrational number and let A*B = C.Suppose their product C, is rational.Then, dividing both sides of the equation by A gives B = A/C.Now, since A and C are both rational, A/C must be rational.Therefore you have B (irrational) = A/C (irrational).Clearly, this is impossible and therefore the supposition must be wrong. That is to say, A*B cannot be ration or, it must be irrational.
Is it possible to completely write out an irrational number in decimal form?
no. irrational numbers are always infininately long, otherwise the could be represented as a fraction by multiplying by 10^n and dividing by 10^n where n is a number large enough to make the number a number with no decimals.
What numbers are rational numbers?
A rational number is any number that can be made by dividing one integer by another.0.5 is a rational number as it can be made by dividing the number 1 by the number 22 is a rational number because it can be made by dividing 2 by 1-6.6 is a rational number because it can be made by dividing -66 by 10---------------------------------------------------------Note there are number that are called irrational numbers. Irrational numbers are all "real" numbers (numbers with a decimal point) that cannot be written as a simple fraction - the decimal goes on forever without repeating.For instance the number Pi is an irrational number.A rational number is a real number that can be expressed as a ratio of two integers. Another way to think about it is this: if you can write a number as a fraction then it's a rational number.
Where was pi found?
The value of pi is found by dividing the circumference of a circle by its diameter and pi is an irrational number which means it can not be expressed as a fraction.
What is the sum of an rational number and irrational number?
An irrational number.
Does dividing an rational number by an irrational number give you an irrational number?
Yes normally it does
Is a number divided by zero irrational?
That is not what mathematicians mean by an irrational number, which is a number with an infinitely long decimal expansion. You will note that since division is the inverse of multiplication, dividing by small numbers has the same effect as multiplying by large numbers, and so dividing by zero, which is an infinitely small number, is equivalent to multiplying by infinity. The result in most cases is deemed to have no mathematical meaning.
Why is the productof a non zero rational number and an irrational number is irrational?
Let A be a non-zero rational number and B be an irrational number and let A*B = C.Suppose their product C, is rational.Then, dividing both sides of the equation by A gives B = A/C.Now, since A and C are both rational, A/C must be rational.Therefore you have B (irrational) = A/C (irrational).Clearly, this is impossible and therefore the supposition must be wrong. That is to say, A*B cannot be ration or, it must be irrational.
Is it possible to completely write out an irrational number in decimal form?
no. irrational numbers are always infininately long, otherwise the could be represented as a fraction by multiplying by 10^n and dividing by 10^n where n is a number large enough to make the number a number with no decimals.
What numbers are rational numbers?
A rational number is any number that can be made by dividing one integer by another.0.5 is a rational number as it can be made by dividing the number 1 by the number 22 is a rational number because it can be made by dividing 2 by 1-6.6 is a rational number because it can be made by dividing -66 by 10---------------------------------------------------------Note there are number that are called irrational numbers. Irrational numbers are all "real" numbers (numbers with a decimal point) that cannot be written as a simple fraction - the decimal goes on forever without repeating.For instance the number Pi is an irrational number.A rational number is a real number that can be expressed as a ratio of two integers. Another way to think about it is this: if you can write a number as a fraction then it's a rational number.
Where was pi found?
The value of pi is found by dividing the circumference of a circle by its diameter and pi is an irrational number which means it can not be expressed as a fraction.
Is irrational numbers closed under division?
Nope. Quick example: e (2.71828) is irrational. Therefore 2*e is irrational making both of them elements of the set of irrational numbers. However, dividing the two, e/(2*e), gives you 1/2, which is a rational number.
What is the sum of an rational number and irrational number?
An irrational number.
Is an irrational number plus an irrational number rational?
No. The sum of an irrational number and any other [real] number is irrational.
The sum of a rational number and an irrational number is?
The sum of a rational and irrational number must be an irrational number.
Is 3.56 an irrational number?
No, 3.56 is not an irrational number. 3.56 is rational.
Whether a rational number multiplied by an irrational number gives an irrational number?
rational * irrational = irrational.
