Need some help

9. Identify each as rational or irrational. Write rational or irrational for each letter on your quiz. (5 points)

8.824

1.4382768….

Part 2:
Mike and Beth both write the decimal 0.as a fraction.
Mike: Beth:
Which student wrote the correct fraction?
How do you know that student is correct?
Describe a mistake that could have been made by the student who wrote the incorrect fraction. (5 points)

I think I did this for you here:

https://www.jiskha.com/questions/1802178/Identify-each-as-rational-or-irrational-Write-rational-or-irrational-for-each-letter

9. 8.824 = 8 824/1000 = 8 103/125 = 1103/1000. Rational.

Part 2: 0/a = 0. a = Any integer except 0.
So 0 is a rational number.

To identify whether a number is rational or irrational, we need to understand the definitions of these terms:

1. Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They can be terminating decimals or repeating decimals.
2. Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They are non-terminating and non-repeating decimals.

Now let's address each part of your question:

1. For the first question, we need to determine whether the given numbers are rational or irrational.

a) ℼ (pi) is an irrational number. It is a mathematical constant that represents the ratio of a circle's circumference to its diameter. Pi cannot be expressed as a fraction, and its decimal representation goes on infinitely without repeating.

b) 8.824 is a rational number. It is a terminating decimal since it ends after the third decimal place. Thus, it can be expressed as a fraction of two integers.

c) 1.4382768… is an irrational number. It is a non-terminating decimal without a repeating pattern, which indicates its irrationality.

Part 2:
To determine which student wrote the correct fraction for the decimal 0., we need to analyze their solutions.

Mike:
Since it is not mentioned what fraction Mike wrote, it is impossible to evaluate whether his fraction is correct.

Beth:
Again, the fraction Beth wrote is not specified in the question, so we cannot determine its correctness.

Without knowing the fractions, we cannot determine which student wrote the correct fraction. The question does not provide sufficient information to decide.

For describing a mistake that could have been made by the student who wrote the incorrect fraction, we need to speculate. Some potential mistakes include:

1. Converting 0. to a fraction using incorrect decimal manipulation or ignoring the decimal point.
2. Incorrectly reducing/simplifying the fraction by dividing both the numerator and the denominator by an incorrect common factor.
3. Ignoring the requirement of expressing the decimal as a fraction altogether and instead providing an unrelated fraction.

Remember, without the actual fractions provided in the question, it is impossible to definitively assess the correctness or mistakes made by either student.