Real Number System

Real Number System

by Miss Jones

​Recall:

​The real number system has SIX different ways that we can classify numbers:

​- Natural (counting)

​- Whole

​- Integer

​- Rational

​- Irrational

​- Real

• ​Natural

  • ​These are (+) whole numbers starting with 1.

• ​Whole

  • ​These are (+) whole numbers starting with 0.

• ​Integer

  • ​These are all (+) and (-) whole numbers and 0.

• ​Rational

  • ​These are numbers that can be turned into a fraction.

• ​Irrational

  • ​These are numbers that cannot be turned into a fraction.

• ​Real

  • ​All numbers that we work with in this class are real. Any number you can find on a number line.

​How to tell a rational or irrational decimal apart.

• ​Rational decimals

  • ​Terminate (end)

  • ​Repeat

​

​

• ​Irrational decimals

  • ​Non-terminating (... or the line above the number)

  • ​Non-repeating

​Remember!

• ​Before classifying a number, make sure it is simplified all the way!

  • ​Reduce, simplify the square roots, etc

• ​0 can be turned into a fraction by putting it over 1.

• ​Any whole number can be turned into a fraction by putting it over 1.

• ​The square root of a number that is NOT a perfect square is IRRATIONAL.

• ​ALL numbers, even IRRATIONAL, are real.

• ​Numbers cannot be IRRATIONAL AND RATIONAL. It's one or the other.

Multiple Select

Irrational decimals are _____ and _____.

• Repeating

• Non-repeating

• Terminating

• Non-terminating

Multiple Select

Rational decimals are _____ and _____.

• Repeating

• Non-repeating

• Terminating

• Non-terminating

Multiple Select

Select all sets that the number belongs to:

-6

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

0.5

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

$$0.\overline{4}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

0.32482418....

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

$$\sqrt{25}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

2

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

0

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

$$\frac{3}{5}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

$$\pi$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to: $$\sqrt{13}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to: $$\frac{2}{3}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to: $$\frac{-10}{2}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

4.00

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

$$-\sqrt{25}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

$$1.\overline{12}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

$$\left|-10\right|$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to: $$\sqrt{3}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to: $$6^0$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:
$$\frac{12}{4}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:
$$\frac{4}{3}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number