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

#### nycfunction

##### Banned
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?

#### HallsofIvy

##### Well-known member
MHB Math Helper
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.)

#### nycfunction

##### Banned
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?

#### Wilmer

##### In Memoriam
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, ...}

#### nycfunction

##### Banned
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.