3 The Numbrella Complex numbers Real Numbers Imaginary Numbers | Rational Numbers Irrational NumbersIntegersWhole NumbersNatural Numbersa+biHas a real and an imaginary componenti—or biCan be expressed as a fractionCan’t be expressed as a fractionAll “non-decimal” valuesAll positive integers and zeroAll positive integers
11 Significant Digits Rules 1-9 are significant0’s between digits are significant0’s at the end suggest rounding and are not significantLeading 0’s are not significant0’s at the end of a decimal indicate the level of precisionEvery digit in scientific notation is significant
12 Examples 1024 4 Significant Digits 1000 1 Significant Digit ALWAYS HAVE ONE SIGNIFICANT DIGIT IN FRONT OF THE DECIMAL FOR SCIENTIFIC NOTATION
13 ExamplesExpand: 2.15 x x 103 a negative exponent tells you to move the decimal to the left Write in scientific notation: 3,145,062 2,230, 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 x x x 10-4
14 ExamplesSimplify: 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 102)(4 x 103) 11 x x 1065 x10 x 108.5 x 10-25 x 10-1
28 What is a proportion and how can you solve a problem with it? 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 = 8x27.5= xSue will earn $27.50 for 5 hours.
31 ExampleIt took the Smith’s 5 hours to go 275 miles. What was their average rate of speed?D=rt275 = r(5)55 = rThey went about 55 mph
32 Work problems Use the reciprocal of the time for the rate of work W for 1st person =hours worked * rate of workW for 2nd person =hours worked * rate of workTotal job always =11 = W for 1st person + W for 2nd person
33 Example: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.
34 EstimationWhat are the critical terms for estimation?
35 The “detail” associated with a measurement PrecisionThe “detail” associated with a measurement
36 Calculations with two different levels of precision can only be accurate to the least precise measure.Add a slide with two examples
37 How correct a measurement is AccuracyHow correct a measurement isThe smaller the unit of measure the more accurate your measurement
38 The amount of difference between your measurement and the true value ErrorThe amount of difference between your measurement and the true value
39 Examples:Jim bought 3 pounds of nails for $ 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