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Complex numbers Real Numbers Imaginary Numbers | Rational Numbers Irrational Numbers | Integers | Whole Numbers | Natural Numbers Can be expressed as a fractionCan’t be expressed as a fraction All “non-decimal” values All positive integers and zero All positive integers i—or bi a+bi Has a real and an imaginary component

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Counting Numbers ◦ 1, 2, 3, 4, 5, …

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Counting Numbers & Zero ◦ 0, 1, 2, 3, 4, 5, …

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Positive and Negative Numbers and Zero ◦ …, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …

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Can be expressed as the ratio of 2 integers

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Cannot be expressed as the ratio of 2 integers ◦ Non-terminating, non-repeating integers ◦Π◦Π

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The approximate value of √7: √4 = 2 √9 = 3 so √7 is approx. 2.6 Determine the approximate value of the point: 1 2 3 4 5 6 7 8 The point is about 3.4

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1-9 are significant 0’s between digits are significant 0’s at the end suggest rounding and are not significant Leading 0’s are not significant 0’s at the end of a decimal indicate the level of precision Every digit in scientific notation is significant

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10244 Significant Digits 10001 Significant Digit .00051 Significant Digit ALWAYS HAVE ONE SIGNIFICANT DIGIT IN FRONT OF THE DECIMAL FOR SCIENTIFIC NOTATION

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Expand: 2.15 x 10 -3 2.15 x 10 3 a negative exponent tells you to move the decimal to the left.002152150 Write in scientific notation: 3,145,062 2,230,000.000345 move the decimal so that there is only one digit in front and count the number of spaces you have moved—moving left is positive here and right is negative. 3.145062 x 10 6 2.23 x 10 6 3.45 x 10 -4

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Simplify: do the math on the numeric portion as you normally would, use the rules of exponents on the powers of ten, place in standard scientific notation to finish (one digit before the decimal) (2.75 x 10 2 )(4 x 10 3 ) 11 x 10 5 1.1 x 10 6 5 x 10 6. 10 x 10 8.5 x 10 -2 5 x 10 -1

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Convert 20% to a decimal 20/100=.2 Convert.45 to a percentage .45 * 100= 45% Convert ¾ to a percentage ¾=.75.75 * 100=75%

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What is 7 percent of 50? ◦.07 * 50 = 3.5 A CD that normally costs $15 is on sale for 20% off. What will you pay ◦ Option 1 .2 * 15 = 315-3= 12 ◦ Option 2 If it is 20% off you will pay 80% .8 * 15 = 12

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ARANTHESISARANTHESIS XPONENTSXPONENTS MULT&DIVMULT&DIV ADD&SUBADD&SUB From left to right

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30 ÷ 10 (20 – 15) 2 30 ÷ 10 5 2 30 ÷ 10 25 75 Parenthesis Exponents then mult and div From left to right

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Absolute value is the distance from the origin and distance is always positive.

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|6||-7||-9-3| 6 7 |-12| 12

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GCF—greatest common factor What is the largest number that divides all the given numbers evenly 20356024 5 4 5 7 6 10 3 8 2 2 2 3 2 5 2 4 2 2 2 2 * 5 5*7 2 2 *3*5 2 3 *3 WHAT DO THEY SHARE? 52 2 * 3=12

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LCM—least common multiple What is the smallest number that the given number go into evenly 20356024 5 4 5 7 6 10 3 8 2 2 2 3 2 5 2 4 2 2 2 2 * 5 5*7 2 2 *3*5 2 3 *3 WHAT IS THE LAGEST VALUE SHOWN IN EACH? 2 2 *5*7=140 2 3 *3*5=120

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If Sue charges a flat rate each hour to babysit. If she ears $44 for 8 hours. What will she earn for 5 hours? PRIMARY RULE: ◦ If you put the $ amount in the numerator on one side put the same value in the numerator on the other side. Etc. cross mult. 220 = 8x 27.5= x Sue will earn $27.50 for 5 hours.

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It took the Smith’s 5 hours to go 275 miles. What was their average rate of speed? D=rt 275 = r(5) 55 = r They went about 55 mph

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Use the reciprocal of the time for the rate of work W for 1 st person =hours worked * rate of work W for 2 nd person =hours worked * rate of work Total job always =1 1 = W for 1 st person + W for 2 nd person

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John and Sam decide to build a bird house. John and build the bird house in 5 hours working alone. Sam can do it in 8 hours alone. How long will it take if they work together? It will take them 3.08 hours to make the bird house.

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What are the critical terms for estimation?

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The “detail” associated with a measurement

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Calculations with two different levels of precision can only be accurate to the least precise measure.

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How correct a measurement is The smaller the unit of measure the more accurate your measurement

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The amount of difference between your measurement and the true value

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Jim bought 3 pounds of nails for $16.25. Which amount is closest to the price per pound? Round off and check above and below 15/3 = 5 and 18/3 = 6 A reasonable values would be between $5 and $6 but closer to $5

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1 inch = 2.54 cm 12 inches = 1 foot 3 feet = 1 yard 5280 feet = 1 mile How many inches are in 1 yard? ◦ 1 yard = 3 feet 1 foot = 12 inches 3x12 =36 inches

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3 Teaspoons = 1 Tablespoon 2 Tablespoons = 1 ounce 8 ounces = 1 cup 2 cups = 1 pint 2 pints = 1 quart 4 quarts = 1 gallon

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16 ounces = 1 pound 2.2 pounds = 1 kilogram 2000 pounds = 1 ton

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milli- centi- -meter = distance -gram = weight -liter = fluid kilo-

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