Which of the following is an irrational number: 25−−√, π, or 027?
An irrational number is a number that cannot be expressed as a fraction (or ratio) of two integers.
Of the options given, the number 25−−√ is not an irrational number because it can be written as the square root of 25, which is 5.
On the other hand, π is an irrational number. It is a mathematical constant, approximately equal to 3.14159, and cannot be expressed as a fraction.
Finally, 027 is not an irrational number because it can be written as the fraction 27/1.
Therefore, the irrational number among the options given is π.
Of the following numbers, which is an integer but does not belong in either of the subsets of integers: −13, 0, or 13?
Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?(1 point)
Responses
rational numbers, integers, whole numbers, natural numbers
rational numbers, integers, whole numbers, natural numbers
irrational numbers, square roots, endless decimals, pi
irrational numbers, square roots, endless decimals, pi
integers, rational numbers, natural numbers, whole numbers
integers, rational numbers, natural numbers, whole numbers
natural numbers, whole numbers, integers, rational numbers
An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers.
Out of the options given, π (pi) is an irrational number. It is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and cannot be expressed as a fraction or a terminating or repeating decimal.
An irrational number is a number that cannot be expressed as a fraction, and its decimal representation goes on forever without repeating. To determine which of the given numbers is irrational, let's examine each one:
1. 25√: To check if this is an irrational number, we need to evaluate its square root. The square root of 25 is 5, which is a rational number since it can be expressed as a fraction (5/1). Hence, 25√ is not an irrational number.
2. π (pi): Pi is a famous example of an irrational number. It is a mathematical constant that represents the ratio of a circle's circumference to its diameter. The decimal representation of pi is non-repeating and goes on forever, thus making it an irrational number.
3. 027: This number can be expressed as a fraction, 27/100, which means it is a rational number. The decimal representation of 027 is not infinite or non-repeating, so it is not an irrational number.
In conclusion, out of the given options, only π (pi) is an irrational number.