Opener 1. Simplify 2. The electricity output of a circuit is modeled 
by the function f(x) = 3( 64 𝑥 ), where x is the time in hours. How much output will there be, in joules, after just 30 minutes?

Opener Change to Rational Exponents 𝒎 𝟒 / 𝟔 x 𝒎 𝟐 / 𝟓 = 𝒎 𝟏𝟔 / 𝟏𝟓 1. Simplify Change to Rational Exponents 𝒎 𝟒 / 𝟔 x 𝒎 𝟐 / 𝟓 = 𝒎 𝟏𝟔 / 𝟏𝟓 Now Re-write as a radical expression…

Opener 3( 64 1 / 2 ) because we have ½ hour 3*√64 = 24 joules 2. The electricity output of a circuit is modeled 
by the function f(x) = 3( 64 𝑥 ), where x is the time in hours. How much output will there be, in 
joules, after just 30 minutes? 3( 64 1 / 2 ) because we have ½ hour 3*√64 = 24 joules

HW ?'s

Essential Question Learning Objective What is the difference between rational and irrational numbers? I will correctly classify numbers, specifically as rational or irrational numbers.

Number System Look at the number on your CARD. We are going to be reviewing the real number system.

Number System THE non-WHOLE #'s WHOLE #'s

Number System THE How would you describe a whole number? WHOLE #'s The numbers {0, 1, 2, 3, ...} etc. There is no fractional or decimal part. And no negatives. Example: 5, 49 and 980 are all whole numbers.

Number System INTEGERS non-INTEGERS THE non-INTEGERS INTEGERS How would you describe an integer? Integers are a special group or category of numbers that: Consist of the set of numbers: {…-4, -3, -2, -1, 0, 1, 2, 3, 4…} Are all positive and negative whole numbers, which do not include any fractional or decimal part.

Number System RATIONAL #'s IRRATIONAL #'s THE IRRATIONAL #'s RATIONAL #'s A number that can be made by dividing two integers. (Note: integers have no fractions.)  The word comes from "ratio". Examples: • 1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2) • 0.75 is a rational number (3/4) • 1 is a rational number (1/1) • 2 is a rational number (2/1) • 2.12 is a rational number (212/100) • −6.6 is a rational number (−66/10) But Pi is not a rational number, it is an "Irrational Number".

So how can we square a number and get a negative result So how can we square a number and get a negative result? Because we "imagine" that we can. The "unit" imaginary numbers (the same as "1" for Real Numbers) is √(-1) (the square root of minus one), and its symbol is i, or j. Number System THE IMAGINARY #'s REAL #'s How would you describe a real number? A number that when squared gives a negative result.  If you square a Real Number you always get a positive, or zero, result. For example 2×2=4, and (-2)×(-2)=4 as well.  The type of number we normally use, such as 1, 15.82, −0.1, 3/4, etc. Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers.  They are called "Real Numbers" because they are not Imaginary Numbers.

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Essential Question Learning Objective What is the difference between rational and irrational numbers? I will correctly classify numbers, specifically as rational or irrational numbers.

What makes a number an irrational number? Closure What makes a number an irrational number? Sent. Starter: "A number is irrational when..."

HW Math II HW#7 Classifying Numbers