# Is (27/4)/(6.75) a Whole, Natural, Integer, Rational, or Irrational Number?

• MHB
• nycfunction
In summary, the fraction (27/4)/(6.75) is a real number and belongs in the set of integers, whole numbers, natural numbers, and rational numbers. It is not an irrational number.
nycfunction
Let Z = set of real numbers

Determine if (27/4)/(6.75) is a whole number, natural number, integer, rational or irrational.

I will divide as step 1.

27/4 = 6.75

So, 6.75 divided by 6.75 = 1.

Step 2, define 1.

The number 1 is whole or natural. It is also an integer and definitely a rational number because it can be expressed as 1/1, which is, of course, 1.

I conclude by saying that (27/4)/(6.75) belongs in the set of Z.

What do you say?

I think that's a very strange way of putting it! Exactly what question are you trying to answer? You say "determine if (27/4)/(6.75) is a whole number, natural number, integer, rational, or irrational." "Real number" is not included in that list so there is no need to say that. Yes, it is a natural number, whole number, integer, and rational number. It is not an irrational number. You don't say that.

(And "Z" is a pretty standard notation for the integers, not the real numbers.)

HallsofIvy said:
I think that's a very strange way of putting it! Exactly what question are you trying to answer? You say "determine if (27/4)/(6.75) is a whole number, natural number, integer, rational, or irrational." "Real number" is not included in that list so there is no need to say that. Yes, it is a natural number, whole number, integer, and rational number. It is not an irrational number. You don't say that.

(And "Z" is a pretty standard notation for the integers, not the real numbers.)

Apparently some typos at my end. Yes, I meant to define Z as integers not real numbers. The question comes from a Cohen precalculus textbook. Basically, in the world of real numbers, (27/4)/(6.75) falls in the category of whole numbers, natural or counting numbers, rational numbers and surely an integer. I say this is correctly stated. You?

nycfunction said:
Apparently some typos at my end. Yes, i meant to define Z as integers not real numbers.
The question comes from a cohen precalculus textbook. Basically, in the world of real numbers, (27/4)/(6.75)
falls in the category of whole numbers, natural or counting numbers, rational numbers and surely an integer.
I say this is correctly stated. You?
z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Wilmer said:
z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Ok. I am right. The fraction (27/4)/(6.75) is a real number. It falls into the category of whole number, natural or counting number, rational, and integer.

## 1. What is the definition of a whole number?

A whole number is a number that is not a fraction or decimal, and is also not negative. It includes all positive integers (1, 2, 3, etc.) and zero (0).

## 2. Is (27/4)/(6.75) a whole number?

No, (27/4)/(6.75) is not a whole number. It is equal to 1.5, which is not a whole number as it is a decimal.

## 3. What is the definition of a natural number?

A natural number is a positive integer (1, 2, 3, etc.) that is used for counting and ordering.

## 4. Is (27/4)/(6.75) a natural number?

No, (27/4)/(6.75) is not a natural number. It is equal to 1.5, which is not a positive integer.

## 5. What is the definition of a rational number?

A rational number is a number that can be expressed as a ratio of two integers (a/b), where b is not equal to 0.

## 6. Is (27/4)/(6.75) a rational number?

Yes, (27/4)/(6.75) is a rational number. It can be expressed as 9/6, where both 9 and 6 are integers and 6 is not equal to 0.

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