Question

Find two rational numbers between -2.3 and -2.33.

Answer 1

Hint: Try to recall the definition of rational and irrational numbers. We can also pick any two random rational numbers that are greater than -2.33 and less than -2.3. Remember that -2.3 is greater than -2.33, even though the relation between the absolute values have the opposite relation.

Complete step-by-step answer:
Before moving to the options, let us talk about the definitions of rational numbers followed by irrational numbers.
So, rational numbers are those real numbers that can be written in the form of $\dfrac{p}{q}$ such that both p and q are integers and $q0$ . In other words, we can say that the numbers which are either terminating or recurring when converted to decimal form are called rational numbers. All the integers fall under this category.
Now, moving to irrational numbers.
Those real numbers which are non-terminating and non-recurring are termed as irrational numbers.
The roots of the numbers which are not perfect squares fall under the category of irrational numbers. $\pi \text{ and }e$ are also the standard examples of irrational numbers.
Now moving to the solution. Let us find two rational numbers, which are greater than -2.33 and less than -2.3. It will be better if we convert both the numbers to their fraction form by multiplying the numerator and denominator by 100. In doing so, our question becomes to find 2 rational numbers lying between $-\dfrac{233}{100}$ and $-\dfrac{230}{100}$ . So, the numbers can be $\dfrac{-232}{100}\text{ and }\dfrac{-231}{100}$ which in decimal form comes out to be -2.32 and -2.31 .

Note: We should also remember that there exist infinite rational and irrational numbers lying between two distinct rational numbers. Also, be very careful about the signs of the numbers which you are asked, as for the above question if the numbers were 2.30 and 2.33, 2.33 would have been greater than 230.