Study guides

☆☆

Q: What is the positive rational number and positive irrational number that are smaller than 0.000001?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

Irrational numbers are infinitely dense so it is not possible to list them. Whatever positive irrational number you select, there are infinitely many smaller ones.

No, they can be as big as you like.

It is NOT necessarily a positive. It will be positive only if it is a larger number minus a smaller number.

No. In fact, larger positive integers never divide smaller positive integers.

Always, and for all basic operations, EXCEPT when you are subtracting the bigger positive number from a smaller positive number.

Related questions

there are infinitely many positive rational and irrational numbers smaller than .0001. Try .00001. Or how about π/100000.

There is no simple answer:Zero is smaller than any positive number.Zero can be larger or smaller than a rational number.A rational number can be larger or smaller than a positive number.

You can choose an irrational number to be either greater or smaller than any given rational number. On the other hand, if you mean which set is greater: the set of irrational numbers is greater. The set of rational numbers is countable infinite (beth-0); the set of irrational numbers is uncountable infinite (more specifically, beth-1 - there are larger uncountable numbers as well).

Irrational numbers are infinitely dense so it is not possible to list them. Whatever positive irrational number you select, there are infinitely many smaller ones.

Nothing special happens. The answer can be smaller or bigger. A rational can become irrational or the other way around.

Because some of them are squares of rational numbers. So their square roots are the rational numbers.Thus if x is rational, then the square roots of x2, which are -x and +x are both rational.

For two rational numbers select any terminating or repeating decimal number which starts with 2.10 and for irrational numbers you require a non-terminating, non-repeating decimal which also starts with 2.10.

1/infinity? * * * * * Nice idea but unfortunately that is not a rational number, which is defined as the ration of two integers, x/y where y > 0. Since infinity is not an integer, the suggested ratio is not a rational number. The correct answer is that there is no such number. If any number laid claim to being the smallest positive rational, then half of that number would have a better claim. And then a half of THAT number would be a positive rational that was smaller still. And so on.

It is the smallest non-negative rational number. Negative numbers are rational and are smaller.

The only generalisation posible is that it will always be a rational number. The product can be positive or negative; it can be a fraction or an integer, it can be larger or smaller.

This question has no solution.We have to begin somewhere.Let us assume that "the first 5" starts from zero,.Zero is rational, so the first irrational must be above zero.How far above zero ?You choose.You construct an irrational just above zero and call that the first.Tell me what it is and I'll guarantee to construct one smaller than that but still above zero.Then someone else will find one smaller than mine.Little fleas have lesser fleas upon their backs to bite 'emAnd lesser fleas have smaller fleas, and so on ad infinitum.

No, they can be as big as you like.

People also asked