Question

rational numbers
a ____________ is a number that can be written as a quotient of two integers.
examples:
integers
the numbers... - 3, - 2, - 1,0,1,2,3... consisting of the negative integers, zero and the positive integers.
whole numbers
any of the numbers (0,1,2,3) etc. there is no fractional or decimal part. there are no negatives.
counting/natural numbers
numbers that can be used for counting things (1,2,3 etc.)

• does not include zero.
• does not include negative numbers.
• does not include fractions.
• does not include decimals.

irrational numbers
an ____________ is a number that cannot be written as a quotient of two integers.
irrational means not rational
examples:
real numbers
a ____________ consists of

• rational numbers
• integers
• whole numbers
• counting/natural numbers
• irrational numbers

place the following words and numbers on the note page.
rational number
real number
irrational number
5
2.75
π
0
3/2
2 1/4
√2
√5
0.33333333...

Explanation:

A rational number is a number that can be written as a quotient of two integers. Integers like - 3, - 2, - 1, 0, 1, 2, 3 etc., whole numbers (0, 1, 2, 3...), counting/natural numbers (1, 2, 3...), fractions like $\frac{3}{2}$ and $2\frac{1}{4}$, terminating decimals like 2.75 and repeating decimals like 0.3333333... are rational. An irrational number cannot be written as a quotient of two integers, examples are $\pi$, $\sqrt{2}$, $\sqrt{5}$. Real numbers consist of both rational and irrational numbers.

Answer:

Rational numbers: 5, 2.75, 0, $\frac{3}{2}$, $2\frac{1}{4}$, 0.3333333...
Irrational numbers: $\pi$, $\sqrt{2}$, $\sqrt{5}$
Real numbers: 5, 2.75, $\pi$, 0, $\frac{3}{2}$, $2\frac{1}{4}$, $\sqrt{2}$, $\sqrt{5}$, 0.3333333...