Rational Numbers Math 8

OBJECTIVE: -You will be able to identify rational numbers -You will be able to write fractions as decimals Word Watch: -rational number -terminating decimals -repeating decimals

PICK YOUR BRAIN!! What is a whole number? What is an integer? Positive whole numbers starting with 0. Ex: 0,1,2,3,4, etc. What is an integer? The numbers …, -4, -3, -2, -1, 0, 1, 2, 3, 4… Consists of negative #’s, zero, & positive #’s.

(In other words, it can be written as a fraction.) A rational number is a number that can be written as where a and b are integers. (In other words, it can be written as a fraction.) Let’s look at the relationship among whole numbers, integers, and rational numbers. a b

Rational #’s Integers Whole #’s _ 0.8 -6 2 -10 13 8 -4 49 1 12 5 -1.44 2 -10 13 8 -4 49 1 12 2 3 5 _ -1.44 5.2

Identify Rational Numbers Show that the number is rational by writing it as a fraction. a) 6 b) c) 0.75 d) 6 1 = 3 5 -3 5 = - 75 100 3 4 = = 1 3 -7 3 -2 =

 YOUR TURN!!  Show that each number is rational by writing it in form. a) 2.5 b) -1 c) -0.8 d) a b 5 2 = -1 1 = -8 10 -4 5 = = 5 8 5 8 =

Writing Fractions as Decimals 7 20 Write as a decimal . 3 5 ______ Write zeros in dividend as placeholders. 20)7.00 60 ____ 100 100 remainder is zero

Write 3 as a decimal What can you tell me about the 3? 5 8 Write 3 as a decimal What can you tell me about the 3? 3 is a whole number. It will be on the left side of the decimal point. 0. 6 2 5 ______ 8)5.000 48 20 16 40 40 3 + 0.625 = 3.625

 YOUR TURN  Write as a decimal Write 3 as a decimal 3 10 0.3 4 5 3.8

VOCAB When a long division problem results in a remainder of 0, the quotient is a terminating decimal. Repeating decimal: where one of more digits repeat without end. Can be written with a bar over the digit(s) that repeat. (bar notation)

Writing Fractions as Repeating Decimals 5 3 Write as a decimal 1. 6 6 6 ______ The digit 6 keeps repeating! 3)5.000 3 20 18 20 18 The remainder will never be zero 20 _ 5 3 = 1.6

Write as a decimal 13 33  The digits 3 and 9 keep repeating 0. 3 9 3 _________ 33)13.000 99 310 297 130 99  Remainder will never be zero 310

 YOUR TURN  7 9 Write as a decimal __ 0.7