It is the smallest non-negative rational number. Negative numbers are rational and are smaller.
1
There is no such number. If any number laid claim to being the smallest rational number its claim could be challenged by half that number - which would also be rational and, obviously smaller. And the claim of that number could be challenged by half that number, and so on.
How about: 0.01
It is 100
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.
There are an infinite number of rational numbers so it would be foolish to even try to list them.
2
It is 1 because it can be expressed as a fraction in the form of 1/1
What is the smallest subset of real numbers that −√𝟑𝟐𝟒 fits best?
It is a rational number. It can be written as a fraction.
There is no such number. The empty set is a subset of rational numbers and, by definition, it contains no numbers so nothing that can be common to any other subset.Alternatively, all rational numbers less than -1 and all rational numbers greater than 1 are subsets of rational numbers. There is no number common to them.