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Transcript
Use Integers and Rational Numbers (2.1) Definition: A Whole Number belong to the set of numbers {0, 1, 2, 3, …}. Whole numbers do NOT have a fractional or decimal part. Whole numbers are NOT negative Is the number a Whole Number? If NOT, explain. Ex. 17 __________________ Ex. 3.4 __________________ Ex. 3 ½ __________________ Ex. -6 ___________________ Ex. 0 ____________________ Ex. ¾ ___________________ Definition: Integers belong to the set of all whole numbers and their opposites {… -3, -2, -1, 0, 1, 2, 3, …} Integers do NOT have a fractional or decimal part. Integers CAN BE Positive or Negative. Is the number an Integer? If NOT, explain. Ex. 17 __________________ Ex. 3.4 __________________ Ex. 3 ½ __________________ Ex. -6 ___________________ Ex. 0 ____________________ Ex. ¾ ___________________ Definition: Rational Numbers belong to the set of all numbers that can be written in the form In other words, a rational number is any number that can be written as a fraction a . b Whole Numbers and Integers can ALL be written as a fraction by putting the number over 1. Ex. 6 = ______ , so 6 is ____________________________ Ex. -9 = ______, so -9 is ___________________________ Proper Fractions and Improper Fractions are already in the form Ex. 3/5 = _______, so 3/5 is __________________________ Ex. 7/3 = _______, so 7/3 is _________________________ Mixed Fractions can be turned into Improper Fractions Ex. 2 ¾ = _______, so 2 ¾ is _______________________ Terminating Decimals can be written as fractions Ex. 0.3 = ________, so 0.3 is _______________________ Ex. 0.23 = __________, so 0.23 is ____________________ Ex. 1.7 = __________, so 1.7 is ________________________ 1 Repeating Decimals can be written as fractions _ _ Ex. 0.3 = __________, so 0.3 is __________________ Rational Numbers Can Be ALL of the Following: Whole Numbers Integers Fractions (Proper and Improper) Mixed Fractions Decimals o Terminating (End) o Repeating **In other words, the only numbers that are NOT RATIONAL are decimals that do NOT TERMINATE (end) or DON’T REPEAT. Rational Numbers Integers Whole Numbers Fractions Decimals Is the number a Rational Number? If NOT, explain. Ex. 17 __________________ Ex. 3 ½ __________________ Ex. -6 ___________________ Ex. 3.4 __________________ Ex. ¾ ___________________ __ Ex. 0.18 _________________ Ex. 0 ____________________ Ex. 0.5 ___________________ Ex. 2.39582034… _________ _ Ex. 0.5 _______________ Ex. Tell whether each of the following numbers is a whole number, an integer, or a rational number: 5, 0.6, - 2 2 /3, -24, 0.45 5 _______________________________________ 0.6 ______________________________________ -24 _____________________________________ __ 0.45 _____________________________________ - 2 2/3 ____________________________________ 2 Understanding Numbers on a Number Line Numbers get bigger to the right Numbers get smaller to the left -5 -4 -3 -2 -1 Negative Numbers 0 1 2 3 4 Positive Numbers 5 0 is neither positive or negative Which number is greater? You may use a number line. Ex. - 4 or 2 ________ Ex. -3 or 0 ________ Ex. -2 or -5 ________ Ex. -2 or 2 ________ Order the numbers from Least to Greatest **If you have to compare fractions and decimals it is easiest to change all of the fractions to decimals to compare. **To change fractions to decimals remember to divide Ex. 3, -1.2, -2, 0 a b= a b _______, _______, _______, _______ Ex. 3.6, -1.5, -0.31, -2.8 _______, _______, _______, _______ Ex. 4.5, _______, _______, _______, _______ -3/4, -2.1, 1/2 Definition: Opposites are two numbers that the same distance from 0 on a number line but are on opposite sides of 0. Definition: The Absolute Value of a number is the distance a number is from 0. The symbol | a | represents the absolute value of a Find the -a and | a | for each Opposites Absolute Value Ex. a = 14 -a = ________ | a | = ________ Ex. a = -6 -a = ________ | a | = ________ Ex. a = -1.23 -a = ________ | a | = ________ 3 4