Question

Write five rational numbers that are less than 2

Answer 1

Hint: We solve this problem by using the definition of a rational number.
Any number that can be represented in the form \[\dfrac{p}{q}\] where \[p,q\in \mathbb{Z},q\ne 0\] is called as rational number.
We use this definition to find rational numbers. We use the condition that all improper fractions are less than 1 which will be less than 2
Improper fractions are the fractions in which the numerator is less than the denominator.

Complete step by step answer:
We are asked to find the f rational numbers that are less than 2
We know that number that can be represented in the form \[\dfrac{p}{q}\] where \[p,q\in \mathbb{Z},q\ne 0\] is called as rational number.
We also know that all improper fractions are less than 1 which will be less than 2
Now, let us take any 5 improper fractions using the definition that in improper fractions the numerator is smaller than the denominator then we get the fractions as
\[\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{5},\dfrac{2}{5},\dfrac{4}{5}\]
Here, we can see that all the above fractions are less than 1 which implies that the above fractions are less than 2
Therefore, we can conclude that the 5 rational numbers that are less than 2 as
\[\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{5},\dfrac{2}{5},\dfrac{4}{5}\]


Note:
We can solve this problem in another method.
We know that all integers are examples of rational numbers.
We are asked to find the rational numbers that are less than 2
So, let us take some integers that are less than 2 as follows
0, -2, -5, -23, -50
Here, we can see that above all numbers are less than 2 which are integers.
We now that all integers can be represented as rational numbers by taking the denominator as 1.
Therefore, we can conclude that the rational numbers that are less than 2 as
0, -2, -5, -23, -50