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Is it possible to divide one rational number by another to obtain an irrational number as a quotient?
Wiki User
∙ 15y ago
No. Rational numbers are defined as fractions of whole numbers. Suppose we have two rational numbers A = m/n and B = p/q. Then their quotient is defined as A/B = (m*q) / (n*p). Since m,n,p and q are whole, the products m*q and n*p are whole as well, making A/B a rational number.
Wiki User
∙ 15y ago
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Is negative 2pi a rational number?
No. The number pi is irrational, and if you multiply an irrational number by a non-zero rational number (in this case, -2), you will get another irrational number.As a general guideline, most calculations that involve irrational numbers will again give you an irrational number.
Is 7.4239 an irrational number?
Rational numbers are those which can be written as one integer over another integer. 7.4329 = 74239/10000 74239 and 10000 are both integers, thus 7.4239 is a rational number. No; 7.4239 is not an irrational number.
What do rational and irrational numbers have in common?
Rational and irrational numbers are part of the set of real numbers. There are an infinite number of rational numbers and an infinite number of irrational numbers. But rational numbers are countable infinite, while irrational are uncountable. You can search for these terms for more information. Basically, countable means that you could arrange them in such a way as to count each and every one (though you'd never count them all since there is an infinite number of them). I guess another similarity is: the set of rational numbers is closed for addition and subtraction; the set of irrational numbers is closed for addition and subtraction.
Is negative 3 over 4 an irrational number?
No. An irrational number is any number that is not a rational number; A rational number is any number that can be expressed as one integer over another integer. negative 3 over 4 is one integer (negative 3) over another integer (4), and so is a rational number.
Is the product of three rational numbers rational or irrational?
A rational number in essence is any number that can be expressed as a fraction of integers (i.e. repeating decimal). Taking the product of any number of rational numbers will always yield another rational number.
Is it possible to divide one rational number by another to obtain an irrational number as the quotient?
It is not possible to divide one rational number by another to obtain an irrational number. A rational number is of the form a/b where a and b are both integers, whereas an irrational is a number which is impossible to express in the previously mentioned way. Let A=(a/b) and B=(c/d) where A and B are both rational numbers. Consider the quotient A/B, this is the same as A(1/B). Rewrite this as (a/b)x(d/c). Assuming we all know basic arithmetic with fractions we can clearly see that the dividend is axd and the divisor is bxc, and the new expression is (axd)/(bxc). Since a, b, c, and d are all integers and the integers are closed under multiplication (two integers multiplied by each other produce another integer) our new expression as a single fraction is one integer over another and it is therefore a rational number.
Why the product of nonzero rational number and a rational number is an irrational?
Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)
How do you turn an irrational number in to a rational number?
Some irrational numbers can be multiplied by another irrational number to yield a rational number - for example the square root of 2 is irrational but if you multiply it by itself, you get 2 - which is rational. Irrational roots of numbers can yield rational numbers if they are raised to the appropriate power
Is negative 2pi a rational number?
No. The number pi is irrational, and if you multiply an irrational number by a non-zero rational number (in this case, -2), you will get another irrational number.As a general guideline, most calculations that involve irrational numbers will again give you an irrational number.
Is 37 squared a rational or irrational number?
372 = 1,369 is an integer; therefore, it is a rational number. In fact, the square of any integer is always an integer; this is because the sum or product of any two integers is an integer. And every integer is a rational number; this is because a rational number is defined as the quotient obtained by dividing one integer into another; and because every integer is the quotient obtained by dividing that integer by the integer 1.
Which irrational number is closest to 6?
Irrational numbers are infinitely dense. That is to say, between any two irrational (or rational) numbers there is an infinite number of irrational numbers. So, for any irrational number close to 6 it is always possible to find another that is closer; and then another that is even closer; and then another that is even closer that that, ...
Why can't numbers be both rational and irrational?
By definition, an irrational number is a number that is not rational, or in other words a number that cannot be expressed as an integer divided by another integer. A number cannot be both "rational" and "not rational."
Irrational number when multiplied by 0.4?
If you multiply an irrational number by ANY non-zero rational number, the result will be irrational.
Why does a rational number plus an irrational number equal an irrational number?
from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that a + b equals a rational number must be wrong.
Can you add two irrational numbers and get a rational number?
Yes - if I had an irrational number x, and I added that to the number (7-x), I would end up with 7.If the number is irrational, it can be subtracted from a rational/integer to make another irrational.
Is 2.25 a rational number?
A rational number is one such that it is "capable of being expressed as an integer or a quotient of integers, excluding zero as a denominator." So you must ask yourself: can 2.25 be expressed as a quotient of integers? In other words, can you divide one integer by another and get 2.25? The answer is yes, because 9 divided by 4 is 2.25. Therefore, 2.25 is a rational number.
Are irrational numbers always integers?
No. An irrational number is one that is not a rational number. A rational number is once that equals one integer divided by another. So an irrational number cannot be represented by one integer divided by another integer, so it cannot be an integer!
