6.5 Comparing, Ordering, and Connecting Rational Numbers Remember to Silence Your Cell Phone and Put It In Your Bag!

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Presentation transcript:

6.5 Comparing, Ordering, and Connecting Rational Numbers Remember to Silence Your Cell Phone and Put It In Your Bag!

Comparing Rational Numbers (in fraction form) Models For, where b>0, iff a<c. For, where b>0 and d>0, iff ad<bc.

Definition of Less Than for Rational Numbers For, iff a rational number exists such that. If, then.

Be able to: Order rational numbers in fraction form Order rational numbers in decimal form

Denseness Property for Rational Numbers Between any two rational numbers there exists at least one rational number. Be able to find rational numbers between two given rational numbers Fraction Form Decimal Form

Converting Decimals to Fractions Be able to: Terminating Decimals  Fractions Repeating Decimals  Fractions

You may omit Scientific Notation

Relationships Among these Sets of Numbers N  W  I  Q Q I W N

What numbers are not Rational Numbers? Every rational number can be expressed as a terminating or repeating decimal. Numbers which cannot be expressed as either repeating or terminating decimals are not rational numbers.

The Set of Irrational Numbers Real numbers which cannot be expressed as either repeating or terminating decimals. Examples:

The Set of Real Numbers {Rational Numbers} ⋃ {Irrational Numbers} = {Real Numbers} Note – The set of rational numbers and the set of irrational numbers are disjoint sets.

What numbers are not Real numbers? _____________ numbers are not real numbers. Examples: