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Grade 9:  The Learning Equation Math

11.01: Rational Number System

 Number Concepts Refresher pp 2-3

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Prerequisite Skills:

 natural numbers, whole numbers, integers, rational numbers, improper fraction, mixed number, quotient Interactive Component Under Construction

Learning Outcomes:

The student will:

Test your knowledge of number systems by completing the following 5-level game:

• Natural Numbers
• Whole Numbers
• Integers
• Rational Numbers
• Irrational Numbers

Review Number Systems above if you need help.  Good Luck!Good Luck!

 Note: The denominator of a fraction converted from a terminating decimal will be a multiple of 2 and/or 5.

 This exercise substitutes the name for counting numbers for natural numbers.  Test your understanding of  whole, natural/counting, integers, rational and irrational number systems. source:  NSU-Math 1030 Unit 1 Section 1a   Author

## Number Systems

The real number system is made up of rational and irrational numbers.

{...-2, -1, 0, 1, 2, ...}
{0, 1, 2, 3,...}
 NATURAL NUMBERS (N) {1, 2, 3,...}
IRRATIONAL NUMBERS
__
(Q)

Number System

Symbol

Origin of Symbol

Description

natural N Natural

1, 2, 3, ...

Improper fractions, powers and square roots may be natural numbers if their standard form is a natural number  For example:

6/2 = 3   52 = 25   √16 = 4

whole W Whole

0, 1, 2, 3, ...

Improper fractions, powers and square roots may be whole numbers if their standard form is a whole number  For example:

9/3 = 3.33... 62 = 36    √49 = 7

integers Z Zahlen

(German for numbers)

...-3, -2, -1, 0, 1, 2, 3, ...

Improper fractions, powers and square roots may be integers if their standard form is an integer number  For example:

-12/3 = -6    82 = 64    √81 = ± 9

rational
Q
Quotient

Any number that can be written as a fraction where the numerator and denominator are integers.  The resulting decimal will be either repeating or terminating.

Improper fractions, powers and square roots may be rational numbers if their st!ndard form is a rational number  For example:

-13/9 = -1.444 ...    8-2 = 0.015625

(√16)/3 = ±1.333...

Note: the denominator of the fraction cannot be zero.

irrational
 _ Q
Not Quotient Any number that cannot be written as a fraction where the numerator and denominator are integers.

Note:  Since irrational numbers cannot be expressed as a fraction they form decimals that are neither repeating nor terminating.

Powers, square roots, and some constants may be irrational numbers if their standard form is an irrational number  For example:

p      √2      √3      √5      √7      √8

Irrational numbers fill the gaps in the rational number line.

real R Real

Includes the rational and the irrational numbers.

Enrichment:

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