Question

Classify the following number as rational or irrational. 0.3030030003……..

Answer 1

Hint: First compare the number whether it can be converted into $\dfrac{p}{q}$ form check about repetition and termination of digits. For every rational number we can write then inform of $\dfrac{p}{q}$ where p and q are integer values. For irrational all the decimals are non-terminating and non-repeating.

Complete step-by-step answer:
We have to classify whether the following number is rational or irrational where the number is 0.3030030003………
First we will explain what is a rational and irrational number and how to classify them.
The rational numbers are numbers which can be expressed as a fraction and also as positive integers, negative integers and 0. It can be written as $\dfrac{p}{q}$ form where q is not equal to ‘O’.
Rational word is derived from the word ratio which actually means comparison between two or more values or integer numbers and is known as fractions. In simple words, it is the ratio of integers.
Example: $\dfrac{3}{2}$ is a rational number.
The irrational numbers are numbers which are not rational. Now let’s elaborate by telling numbers can be written as decimals but not in fractions which means it cannot be written as a ratio of two integers.
Irrational numbers have endless non-repeating digits after the decimal point.
Example: $\sqrt{8}=2.828.......$
Let us see how to identify rational and irrational numbers based on a set of examples. As per the definition the rational numbers include all integers’ fractions and repeating decimals. For every rational number we can write then inform of $\dfrac{p}{q}$ where p and q are integer values. For irrational all the decimals are non-terminating and non-repeating.
In the question we are given,
0.3030030003……….
So by analyzing the decimal number can be said as non-repeating and non-terminating hence it is an irrational number.
0.3030030003………… is irrational.

Note: Students should know the definition and basics of rational and irrational numbers. They should know how to classify rational and irrational numbers.