7. Among the following, an irrational number is: a) 0.15 b) 0.1516 c) 0.1
Answer (1)
To determine which number among the given options is an irrational number, let's first understand the difference between rational and irrational numbers.
Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. They can be either finite decimals or repeating decimals. For example, 0.15 is a finite decimal and can be written as 100 15 or 20 3 , which is a rational number.
Irrational numbers, on the other hand, cannot be expressed as a simple fraction. Their decimal representation is neither finite nor repeating—it continues indefinitely without a repeating pattern. Examples of irrational numbers include π and 2 .
Now, let's evaluate each option:
Option a: 0.15
This is a finite decimal and can be rewritten as 20 3 . Thus, it is a rational number.
Option b: 0.1516
This number is also a finite decimal, which means it can be represented as a fraction (in this case, 10000 1516 ). Therefore, it is rational.
Option c: 0.1
This is a finite decimal that can be represented as a fraction ( 10 1 ), so it is also rational.
As none of the given options are irrational, the question might be intended to include different types of numbers to identify irrational numbers. However, if you are solely considering the options listed, all are rational numbers, and there is no irrational number among them under typical mathematical definitions.
