Mathematics
Grade-8
Easy
Question
Identify the irrational among the given numbers
- 0.4014001400014…
- 0.14
Hint:
Terminate decimal refers to a decimal with a finite number of digits after the decimal point.
A recurring decimal refers to a decimal with a repeated digit or digits at the end after the decimal point.
Rational numbers refer to those numbers that can be represented as a simple fraction and can be either a whole number, a terminating decimal or a non terminating recurring decimal.
Irrational numbers refer to those numbers that cannot be represented as a simple fraction and are non-terminating non-recurring decimal.
The correct answer is: 0.4014001400014…
TO FIND-
Irrational number from the given options.
SOLUTION-
From the given options, to find the irrational number, we find the option that is a non-terminating, non-recurring decimal.
Option a i.e. 0.1416 which has a bar on top of 16, meaning that 16 is being repeated indefinitely.
Hence, option a is a non-terminating, recurring decimal.
Hence, option a is a rational number.
Option b i.e. 0.4014001400014 is a non-terminating and non-recurring decimal.
Hence, option b is an irrational number.
Option c i.e. 0.1416 which has a bar on top of 1416, meaning that 1416 is being repeated indefinitely.
Hence, option c is a non-terminating, recurring decimal.
Hence, option c is a rational number.
Option d i.e. 0.14 is a terminating decimal.
Hence, option d is a rational number.
FINAL ANSWER-
Option 'b' i.e. '0.4014001400014…' is the correct answer to the given question.
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