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Course: 8th grade (Illustrative Mathematics)>Unit 8

Lesson 5: Extra practice: Irrational numbers

Classifying numbers review

Review whole numbers, integers, rational, and irrational numbers.  Then, practice identifying each.

Whole numbers

start color #1fab54, start text, W, h, o, l, e, space, n, u, m, b, e, r, s, end text, end color #1fab54 are numbers that do not need to be represented with a fraction or decimal. Also, whole numbers cannot be negative. In other words, whole numbers are the counting numbers and zero.
Examples of whole numbers:
4, comma, 952, comma, 0, comma, 73

Integers

start color #11accd, start text, I, n, t, e, g, e, r, s, end text, end color #11accd are whole numbers and their opposites. Therefore, integers can be negative.
Examples of integers:
12, comma, 0, comma, minus, 9, comma, minus, 810

Rational numbers

start color #7854ab, start text, R, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end text, end color #7854ab are numbers that can be expressed as a fraction of two integers.
Examples of rational numbers:
44, comma, 0, point, start overline, 12, end overline, comma, minus, start fraction, 18, divided by, 5, end fraction, comma, square root of, 36, end square root

Irrational numbers

start color #ca337c, start text, I, r, r, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end text, end color #ca337c are numbers that cannot be expressed as a fraction of two integers.
Examples of irrational numbers:
minus, 4, pi, comma, square root of, 3, end square root

How are the types of number related?

The following diagram shows that all whole numbers are integers, and all integers are rational numbers. Numbers that are not rational are called irrational.

Practice

Problem 1
• Current
What type of number is square root of, 5, end square root?

Want to try more problems like this? Check out these exercises:
Classify numbers: rational & irrational
Classifying numbers

Want to join the conversation?

• I've been searching everywhere on Khan Academy for this: What is a natural number, and is there a place on KA where I can find something about this?
• The natural numbers are all whole numbers, excepting 0. 0 is a whole number but not a natural number because it does not have a positive or negative value.
• why is -5 not a whole number its is a type of number ?
• Whole numbers are numbers which are not FRACTIONS , DECIMALS or NEGATIVES.
They are numbers from 1 to Infinity and 0. [0, 1, 2, 3 ...]

While -5 is neither a FRACTION nor a DECIMAL , it is still a NEGATIVE for which it is not a WHOLE number.

Negative Non-Fractional,Non-Decimal numbers are not whole numbers.
Only Positive Non-Fractional,Non-Decimal numbers are whole numbers including Zero.

Integers are the numbers which include both WHOLE numbers and their NEGATIVES (Non-Fractional,Non-Decimal Negatives). [... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ...]
So -5 obviously falls under that category.

Therefore,
-5 is an Integer , not a Whole number !

Hope it helps !
• what type of number is .33%
• It is rational. A percent that is equal to .0033 as a decimal and 33/10000 as a fraction.
• what are non terminating numbers?
• They are numbers like pi, √2, etc. When you express these numbers in decimals, they never stop. These are called irrational numbers. Also, infinity is also not terminating. (Technically, it's not a number. It's just a statement that the number is getting bigger.)
• Are all square rooted numbers irrational?
• Not all square roots are irrational like the square of 9 is three or the square root of 16 is 4 but a lot of numbers are irrational. The square root of a number is if it multiplies by self to get that number. (Like 5*5=25 and the square root of 25 is 5). I hope that makes sense!!
• Would it be accurate to say that whole numbers are positive numbers and zero?
• This is partially correct. The whole numbers are the positive integers and zero. (Note that for example, 1/2 is a positive number that is not a whole number.)

Have a blessed, wonderful day!
• I dont really understand classyfing numbers .
• Classifying numbers is the act of putting numbers into categories, which is why there are so many subsets or the Real Numbers, like the Integers or the Whole Numbers. Putting them into categories is actually quite easy. Natural Numbers are all positive numbers except 0 (1-infinity), Whole Numbers are Natural Numbers + 0 (0, 1-infinity), Integers are Whole Numbers + Negative Numbers (-1, 0, 1, etc...), and Rational Numbers are any number that can be expressed as a fraction. There are also Irrational Numbers, which are a variety of things, but all the subsets I just listed are the main subsets, but there are more than those.

Hope this helps!
• Why is a fraction rational?