Question

State true or false? Zero is the smallest rational number.

Answer 1

Hint: To check whether a given statement is true or false, we need to analyse the given statement and compare it with various examples. Here zero may be a rational number but we need to check for examples of rational numbers less than zero. Only then we can conclude whether the statement is true or false.

Complete step-by-step answer:
We are given a statement and asked whether it is true or false
The first thing we need to do is analyse the given statement and refer to it with different examples and then come to a conclusion.
The given statement is zero is the smallest rational number.
By the classification of numbers, we know that it is classified as real and imaginary.
Which is further classified as rational and irrational numbers
We clearly know that that rational numbers include all integers and fractions
For example, $2,0,\dfrac{3}{5}, - 9$
From this it is clear that zero is a rational number.
Now we need to analyse the fact whether it is the smallest rational number.
As already said, rational numbers consist of integers, both positive and negative.
Considering only positive integers zero may be a small number
But we even have negative integers and it is clear that they are smaller than zero.
Negative integers are rational numbers as well as they are smaller than zero. This proves that there are rational numbers smaller than zero.
For example, $ - 6, - 9, - 8, - 7$
So, zero cannot be the smallest rational number.
Hence the given statement is false.

Note: Many students tend to say the statement is true as zero is a small number. But it is the smallest only when positive integers are considered. But when we talk about rational numbers together then both positive and negative numbers come into account. Now zero cannot be the smallest as it is greater than the negative numbers.