Identify each as rational or irrational. Write rational or irrational for each letter on your quiz. (5 points)
ℼ
8.824
27
1.4382768….
9
π is irrational
if 1.4382768…. shows that the decimal repeats without some type of pattern, then it is also irrational
All the others are rational.
To determine whether each number is rational or irrational, we need to understand the definition of rational and irrational numbers.
Rational numbers are numbers that can be expressed as the quotient or ratio of two integers, where the denominator is non-zero. In other words, rational numbers can be written as fractions.
Irrational numbers, on the other hand, cannot be expressed as a fraction or a ratio of two integers. They are non-repeating and non-terminating decimal numbers that cannot be written as exact fractions.
Now let's analyze each number from the given list:
ℼ (Pi): Pi is an irrational number since its decimal representation goes on forever without repeating.
8.824: This number is rational because it can be expressed as a fraction: 8824/1000, which simplifies to 22/25.
27: This number is rational because it can be expressed as a whole number and, therefore, as a fraction: 27/1.
1.4382768...: This number is irrational because its decimal representation goes on forever without repeating.
9: This number is rational because it can be expressed as a whole number and, therefore, as a fraction: 9/1.
So, to summarize:
ℼ: Irrational
8.824: Rational
27: Rational
1.4382768...: Irrational
9: Rational