Question

Which of the following could be an irrational number?

a) -5
b) 149
c) 2.6457...
d) 3.14765

Answer 1

The correct answer is option c) 2.6457... because it represents a non-repeating, non-terminating decimal that cannot be expressed as a fraction of two integers, which defines it as an irrational number.

Step-by-step explanation:

The correct answer is option c) 2.6457.... To determine if a number is irrational, we look for a pattern that does not terminate or repeat indefinitely. Rational numbers can be written as a simple fraction of two integers. Let's analyze each option:

• -5 is an integer and can be expressed as -5/1, which is a ratio of two integers.
• 149 is also an integer and can be expressed as a fraction, 149/1.
• 3.14765 is a decimal number, but it terminates, so it can be expressed as a fraction.
• 2.6457... with the ellipsis indicates a non-repeating, non-terminating decimal, which cannot be expressed as a fraction of two integers and is therefore an irrational number.

In this context, having an ellipsis '...' after a decimal means the number continues indefinitely without repeating a pattern, defining it as an irrational number.