A decimal number that has digits that repeat forever.

Transcription

1 1.1 Expressing Rational Numbers as Decimals EQ: How do you rewrite rational numbers and decimals, take square roots and cube roots and approximate irrational numbers? What is a terminating decimal? A decimal number that has digits that do not go on forever What is a terminating decimal? A decimal number that has digits that repeat forever

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3 1.1 Expressing Decimals as Rational Numbers EQ: How do you rewrite rational numbers and decimals, take square roots and cube roots and approximate irrational numbers? Decimal to Fraction Look at the last digit and determine the place value..375 = 375 = 75 =

4 1.1 Expressing Decimals as Rational Numbers EQ: How do you rewrite rational numbers and decimals, take square roots and cube roots and approximate irrational numbers? Repeating Decimal to Fraction 1. Let x = the number 2. Identify the place value of the last repeating digit. 3. Multiply (by 10, 100, 1000) 4. Subtract x 5. Divide

5 1.1 Finding Square Roots and Cube Roots EQ: How do you take square roots and cube roots? Square Root There are two square roots for every positive number. 6 2 = 36 and ( 6 2 ) = = ±6

6 1.1 Finding Square Roots and Cube Roots EQ: How do you rewrite rational numbers and decimals, take square roots and cube roots and approximate irrational numbers? Cube Root There is one cube root for every positive number. The cube root of 8 is 2 because. 2 3 = = = 8

7 1.2 Classifying Real Numbers EQ: How can you describe relationships between sets of real numbers? Real Numbers Set of rational numbers and irrational numbers.

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9 1.3 Comparing Irrational Numbers EQ: How do you order a set of real numbers? Compare Real Numbers Use perfect squares to estimate the square root = = 4 A number between 1 and 2.

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13 2.1 Simplifying Expressions with Powers EQ: How can you develop and use the properties of integer exponents?

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16 2.2 Scientific Notation with Positive Powers of 10 EQ: How can you scientific notation to express very large quantities? Scientific Notation Move the decimal behind the first number and drop the zeros. Count the number of places the decimal was moved = 1.23 x 10 11

17 2.3 Scientific Notation with Negative Powers of 10 EQ: How can you use scientific notation to express very small quantities? Scientific Notation Move the decimal after the first nonzero number. Count the number of places the decimal was moved. When the number is between 0 and 1 the exponent is negative.

18 3.1 Representing Proportional Relationships with Equations EQ: How can you use tables, graphs and equations to represent proportional situations? Proportional Relationship Constant of Proportionality Ratio of one quantity to the other is constant. Described by one of these equations: y = kx k = y x

19 Representing Proportions with Equations Step 2 For the number of hours, write the relationship of the amount earned and the number of hours as a ratio (another word for ratio: ) in simplest form. k = y x amount earned number of hours Is the relationship proportional? Yes / No Explain.

20 Representing Proportions with Equations Step 3 Write an equation Let x = amount earned Let y = number of hours Use the equation y kx The equation is: y 12x

21 3.1 Representing Proportional Relationships with Graphs EQ: How can you use tables, graphs and equations to represent proportional situations? Proportional Graph Graph will be a line that goes through the origin (0,0).

22 Representing Proportions with Graphs The graph shows the relationship between the weight of an object on the Moon and its weight on Earth. Write an equation for this relationship. Step 1 Use the points on the graph to make a table. Earth weight (lbs) Moon weight (lbs)

23 Representing Proportions with Equations Step 2 Find the constant of proportionality. k = y x Moon weight Earth weight The constant of proportionality is:

24 Representing Proportions with Graphs Step 3 Write an equation Let x = weight on Earth Let y = weight on Moon Use the equation y kx The equation is: y 1 6 x

25 Rate of Change 3.2 Rate of Change EQ: How do you find a rate of change? chg. in dependent variable ( y) chg. in independent variable ( x) Example The cost is $0.75 per Snickers. constant rate Dependent variable y.75x b Independent variable The cost depends on the number you buy.

26 Rate of Change Eve keeps record of the number of lawns she has mowed and the money she has earned. Tell whether the rates of change are constant or variable. Step 1 Identify the independent and dependent variables. # of lawns Independent Variable $ earned Dependent Variable The amount earned depends on the Explain number of lawns mowed.

27 Rate of Change Step 2 Find the rates of change Day 1 to Day 2: change in $ change in lawns Day 2 to Day 3: Day 3 to Day 4: change in $ change in lawns change in $ change in lawns The rates of change are constant. / are not constant. Price per lawn is. $15.

28 3.2 Slope EQ: How do you find the slope of a line? Slope (m) The steepness of a line. m rise run y x y 2 1 x 2 1 x x x x

29 Method 1 Label ordered pairs 1,4 3, 5 x, y x, y y y m x x Write down formula Substitute values m

30 Method 2 Write ordered pairs 1, 4 3, 5 Subtract y values and x values

31 Method 3 Plot the points 1, 4 3, 5 Find the rise / run

32 Rate 3.3 Interpreting Unit Rate as Slope EQ: How do you interpret the unit rate as slope? Unit Rate Ratio comparing quantities measured in different units. Ratio where the second quantity is 1. Example $ per orange oranges per $1 dollars oranges $2 10 $ oranges dollars $2 2 $1

33 A storm is raging on Misty Mountain. The graph shows the constant rate of change of the snow level on the mountain.

34 4.2 Determining Slope & Y-intercept EQ: How can you determine the slope and y-intercept of a line? y = mx + b Slope Intercept Form of an Equation slope y-int Rate of Change Start value

35 Find the slope (m) and Y-intercept (b). change in y change in x = change in y change in x = change in y change in x = The rate of change (m) is The start value (b) is

36 4.2 Determining Slope & Y-intercept EQ: How can you graph a line using the slope and y-intercept? y = mx + b slope y-int Step 1 Identify m and b Step 2 Plot the point of the y- intercept. Step 3 Use the slope to find a second point.

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38 4.4 Proportional and Nonproportional EQ: How can you distinguish between proportional and nonproportional situations? Proportional Nonproportional y = mx Line goes through the point (0,0) y = mx + b Starting point of line is the y-intercept