171 Views

Download Presentation
## Using Math and Critical Thinking

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Using Math and Critical Thinking**Metric System Scientific Notation**APES Mathematics Review**The APES exam will require you to do mathematical calculations. You will not be allowed to use a calculator. Occasionally these calculations may be possible for you to do in your head; nonetheless, it is MANDATORY to show all work for the calculations on the free response part of the APES exam.**International System of Measurement**Metric Conversions**The International System of Measurement is used by most**people worldwide. (SI) • Only a few countries do not use the metric system and the U.S. is one. • However, the metric system is used by the U.S. scientific community. • In APES most all of the measurements are metric. If in doubt, use the metric system. Metric Conversions**No fractions are involved!**• No Naked Numbers! That means all answers must include units. There is no meaning to 56.8 Two Rules for the International System**King Henry Died Unfortunately Drinking Chocolate Milk**• Kilo K • Hecto H • Decka D • Meter/Liter/Gram M/L/G • deci d • centi c • milli m Metric Prefixes Table**Conversion from larger to smaller units:**• Meters to millimeters • M > mm • Move decimal to right • Three places • 56.8m = _____mm • Conversion from smaller to larger units? • Centimeters to kilometers • cm < Km • Move decimal to the left • 5 places • 4,885 cm = ______km Metric Problems**Introduction**• Not only will you use the metric system, you will also do some slightly more complicated math requiring scientific notation and critical thinking skills.**Scientific Notation**• Very large and very small numbers are more easily manipulated when they are converted to logarithms to the base 10. • Basic fact 100 =1,101 =10, 102 =100, 10-1 =.1 • Usually expressed by placing only one digit to the left of the decimal place. • 1,800,000,000,000 = 1.8 X 1012 • .000000178 = 1.78 X 10-7**WS Conversions 1**• Express one billion in scientific notation. • Express 2,360,000 in scientific notation. • Express 23,000,000,000,000 (23 trillion) in scientific notation.**Scientific Notation**• Multiplication • Multiply the bases and add the exponents • (3 X 103) X (4 X 105) • (3) (4) = 12 • 3 + 5 = 8 • 12 X 108 • 1.2 X 109**Divide the number in the numerator by the number in the**denominator and subtract the exponent of the denominator from the exponent of the numerator. • NUMERATOR/DENOMINATOR • (5.2 x 104) divided by (2.6 X102) • 5.2 divided by 2.6 = 2 • 4-2 = 2 • 2 X 102 Division**Multiply the coefficients**• Add exponents • Ex. (3 X 104)X(2 X 105) = • 6 X 109 • EX. (6 X 105)X(7 X 106) = • 42 X 1011 • 4.2 X 1012 Multiplication**Addition**• Convert both numbers to the same exponent. • Add the numbers. • Convert to scientific notation. • 3,000,000,000 + 14,000,000 • 3000 X 106 + 14 X 106 • 3014 X 106 • 3.014 X 109**Subtraction**Convert both numbers to the same exponent. Subtract the numbers. 3,000,000,000 – 14,000,000 3000 X 106 – 14 X 106 2986 X 106 2.986 X 109**It is often necessary to round numbers in environmental**problems to get reasonable answers. • If the answer is in dollars and cents, it should be rounded accordingly. • $16. 43 NOT $16. 4321 • If the answer is a person or other living organism, it should be rounded accordingly. • 4,037 people NOT 4,037.345 people Rounding**Mean (average)**• Add the numbers and divide the number of numbers. • Median (middle) • Add the number of numbers +1 and divide by 2 to find the middle. • If there are an even number of numbers, the median is the mean of the middle two numbers. • Mode • The number that appears most often. If all the numbers appear the same number of times, there is no mode. Mean, Median, Mode