The Real Number System and Comparing Review

Unit 6:

Numerical Representations & Relationships

Real Number System

• All numbers are Real #'s

• Rational: Any # that can be written as a fraction (Includes decimals that are terminating or repeating & perfect squares)

• Integers: Positive & Negative numbers.

• Whole: Positive numbers including zero.

• Natural (Counting): Positive numbers NOT including zero.

• Irrational: Includes non-repeating/non-terminating decimals, anything with pi, imperfect squares.

Multiple Choice

Which Venn diagram correctly describes the relationship between Set R and Set W?

R = {real numbers}

W = {whole numbers}

• all real #'s are whole numbers #'s

• all whole #'s are real numbers #'s

• some whole #'s are not real numbers #'s

• whole #'s & real numbers #'s not related

​Approximating Real Numbers

Multiple Choice

• Point M

• Point N

• Point P

• Point Q

​Scientific Notation

• If going from scientific notation to standard form, just put it into your calculator.

• If going from standard form to scientific notation, use the steps below. You can still check your work with the calculator to see if your answer matches the standard form.

Fill in the Blank

There are a total of 463,100 books in a library. What is the value of the exponent when this number is written in scientific notation?

​Ordering Real Numbers

• Determine if you are ordering numbers from least to greatest (ascending) or greatest to least (descending).

• Convert all numbers into decimal form.

• Remember that the bigger the negative the smaller the value.

• If you have several numbers that are close in value, write numbers down, add zeros as placeholders, and compare decimal place value.

Multiple Choice

• Rectangle T, Rectangle S, Rectangle P

• Rectangle T, Rectangle P, Rectangle S

• Rectangle S, Rectangle T, Rectangle P

• Rectangle S, Rectangle P, Rectangle T