Scientific Notation and Units of Measurement

Scientific Notation Scientists often deal with both very large and very small numbers. Scientists often deal with both very large and very small numbers. Ex or 100,000,000,000,000,000 To keep things simple, we express these numbers as powers of 10. To keep things simple, we express these numbers as powers of 10. Scientific Notation

Scientific Notation (cont.) Scientific notation is expressed as: Scientific notation is expressed as: M x 10ª M x 10ª Any number between 1 & 10 Power of 10 “a” determines the number of powers

Scientific Notation (cont.) Example = 2.5 x 10 6 Example = 5 x Decimal behind # = right to left = positive 10 power Decimal in front of # = left to Right = negative 10 power

Class Practice: 1. Convert 31,000 to scientific notation. 2.Convert to scientific notation. Scientific Notation (cont.) 3.1 x x 10 -4

You can also convert scientific notation back to standard notation. You can also convert scientific notation back to standard notation. Scientific Notation (cont.) Example x 10 5 = 140,000 Example x = Just move the decimal back in the opposite direction

Multiplying numbers in scientific notation: Multiplying numbers in scientific notation: Scientific Notation (cont.) (4.4 x 10 6 ) x (3.9 x 10 4 ) = 4.4 x 3.9 = = x 10 11

Dividing numbers in scientific notation: Dividing numbers in scientific notation: Scientific Notation (cont.) (5.76 x 10 9 ) ÷ (3.2 x 10 3 ) = 5.76 ÷ 3.2 = – 3 = x 10 6

Units of Measurement 2 systems of measurement in use 2 systems of measurement in use English ( yards, gallons, miles, feet) English ( yards, gallons, miles, feet) Metric (meters, liters, kilometers) Metric (meters, liters, kilometers) Scientists use this system!!!

Why is it important that we know what system we are using? Why is it important that we know what system we are using? Units of Measurement (cont.) MARS STOP SPLAT NASA orbiter (1999): 125 million dollar conversion error!!!

gLmgLm deci centi milli (d) (c) (m) kilo hecto deca (k) (h) (da) Units of Measurement (cont.) Ex g = kg Ex L = mL Ex hg = mg ,000 25,000, x kg 2.5 x 10 5 mL 2.5 x 10 7 mg