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Rational numbers include integers, and any number you can write as a fraction (with integers in the numerator and denominator). Most numbers that include roots (square roots, cubic roots, etc.) are irrational - if you take the square root of any integer except a perfect square, for example, you'll get an irrational number. Expressions involving pi and e are also usuallyirrational.

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Q: Tell whether each number is rational?

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Each of the two numbers is a rational number.

Not necessarily.

I have no idea what "compersion" means or what you are trying to say. A rational number is so called because it can be expressed as ratio of two integers. Each rational number is a ratio and each ratio is a rational number. However, the relationship is not one of equivalence: each rational number can be represented by infinitely many equivalent ratios.

It is each one of them.

Yes. This is the same as asking for one rational number to be subtracted from another; to do this each rational number is made into an equivalent rational number so that the two rational numbers have the same denominator, and then the numerators are subtracted which gives a rational number which may possibly be simplified.

Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational. 1.a +b =c Where a and c are rational and b is irrational. 2.b=c-a Subtracting the same number a from each side. 3.b is irrational c-a is a rational number we arrived at a contradiction. So the sum is an irrational number.

Not quite. A rational number is a ratio and each rational number is a ratio of specific pairs of integers - not ANY two integers. And, of course, 0 is not allowed on the denominator.

A number is prime if it only has two distinct factors.

Each and every rational number except 0. Once you leave the domain of integers, all rational numbers (excluding 0) divide into every other rational number with a quotient that is rational. The above can be extended to real numbers.

They can all be represented by ratios of two integers.

101, 173 and 911 are all prime numbers. 173911 is not.

Do you mean can we subtract one rational number from another rational number and get an irrational number as the difference? I'm not a mathematician, but I suspect strongly the answer is no. Wouldn't this imply that we can sometimes add a rational number to an irrational one, and get a rational number as a sum? That doesn't seem possible.Ans 2.It isn't possible. Proof :-Given two rational numbers, multiply the two denominators.Express each rational in terms of the common multiple.Algebraically add the numerators of the new rational numbers.Put this over the common multiple; there's the result expressed as a ratio.

In theory it is possible but in practice, if a number is a product of two very large primes - each being a hundred digits long, or larger - then it is very difficult to tell whether it is prime or composite. The fact that it is so difficult makes this characteristic particularly useful for data encryption.

It is not an irrational number but is each of the others.

Rational numbers are of the form n/m where n and m<>0 are integers. Since for each integer n and integer 1 we know that n = n/1, each integer is a rational number.

The atomic number of an element is the number of protons in each atom of the element, whether neutral or not. If the atom is neutral, the number of electrons in the atom is the same as the number of protons.

That terminating decimal 0.2020020002 is a rational number and is: 2020020002/10000000000 = 1010010001/5000000000 If you mean a non-terminating decimal 0.2020020002.... where each 2 is followed by one more zero than the previous 2 then it is not a rational number.

Any natural number, such as 37, will also be in each of the other categories.

Any 2 digit integers are rational numbers because all integers or whole numbers are rational numbers.

Yes, for example, square root of 2 x square root of 2 = 2.* * * * *No, the product of two rational numbers must always be rational.No.Proof :If you take rational number a/b and multiply by rational c/d you get ac/bd.Since ac and bd are each integral, the product is rational.

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number of each atom

23

Rational numbers are those decimals which either terminate or end in a repeating sequence of 1 or more digits. Assuming the number continues with an extra 0 before the next 8 each time then the number neither terminates nor ends in a sequence of repeating digits, thus it is not a rational number.