If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Class 9 (Old)>Unit 1

Lesson 1: Irrational numbers

# Classifying numbers

There are many categories we can use to classify numbers. Some of those categories are rational numbers, irrational numbers, integers, and whole numbers. Rational numbers are represented as a fraction of two integers, while irrational numbers cannot be represented as a fraction of two integers. Integers are positive and negative numbers that don’t involve fractions or decimals. Whole numbers are a subset of integers — they are non-negative integers.

## Want to join the conversation?

• can someone give me a summary of natural numbers, whole numbers, integers, rational numbers ad irrational number please? i'm still kinda confused because i'm not sure about the differences between them
• Natural numbers:
all the whole numbers except 0

Whole numbers:
all of the counting numbers (1, 2, 3, etc.) plus 0

Integers:
(can be positive or negative)
all of the whole numbers (1, 2, 3, etc.) plus all of their opposites (-1, -2, -3, etc.) and also 0

Rational numbers:
any number that can be expressed as a fraction of two integers (like 92, -56/3, √25, or any other number with a repeating or terminating decimal)

Irrational numbers:
all the numbers that can't be expressed as a fraction of two integers (like π, √7, or any other number with a non-repeating & non-terminating decimal)

Hope this helps!
• Why is 0 considered rational if 0/0 is undefined? i guess it can be integer because its sign neutral. I would assume its just a whole number and an integer.
• The fact that 0 can be written as 0/1 is enough to show that 0 is rational.
• wait, aren't whole numbers literally the same thing as integers? and inside integers you have natural numbers, so it'd be, reals => rational and irrational, within rational => integers => natural numbers and then outside reals, complex.

how are whole numbers in any way different from integers? or natural, for that matter? or is it just a different name? but N is used for them, so it should be "natural", still.
• natural numbers contains just the positive numbers.
whole numbers are different as they contain zero in addition.
Integers are also different they contain negative numbers ,positive numbers and 0.
• How is pie over pie one!?!?!!?!?!?! Pie is inf
• While pi has an infinite number of decimal digits, pi is overall still a finite number because pi is between 3 and 4.

Any nonzero, finite number divided by itself is 1.

So pi / pi = 1.

Have a blessed, wonderful day!
• Doesn't it mean that integers are only negative?
• Integers are 1,2,3,4,5,6,7,8,9, e.t.c. They can also be negative, but-
• what a minute how come a couple of fractions are just in the rational section while 1 of them is in the whole number section?
• To classify the numbers, we need to look at them in simplified form.
`14/7` simplifies to `2`, which is a whole number. The other fractions do not simplify down to whole numbers, so they only fit in the Rational Number classification.
• Tell me why I NEED to classify a number?
• Study= to good grades=happy=more free time= more study= better grades= early graduation = happy and college= sad = study = good grade = happy = better grade = happy and graduation in feild = job = life = more work = sad = no grades to do = sadder = old = happy bc no job = live long = end (if u know u know)
(1 vote)
• Is pi infinite? if not will anybody know the last numbers of it? also can a rational number be a irrational number just in its prime and the other way around?
• Yes, π (or "pi") has a non-repeating decimal that goes on forever.

Rational numbers cannot be irrational, because a number can only be one or the other.

Hope this helps!