1. Scientific Notation and Units of Measurement

2. 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. 0.00000000000000001 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

3. 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

4. Scientific Notation (cont.) Example 1. 2500000 0= 2.5 x 10 6 Example 2. 000005 = 5 x 10 -5 Decimal behind # = right to left = positive 10 power Decimal in front of # = left to Right = negative 10 power

5. Class Practice: 1. Convert 31,000 to scientific notation. 2.Convert 0.00012 to scientific notation. Scientific Notation (cont.) 3.1 x 10 4 1.2 x 10 -4

6. You can also convert scientific notation back to standard notation. You can also convert scientific notation back to standard notation. Scientific Notation (cont.) Example 1. 1.4 x 10 5 = 140,000 Example 2. 1.5 x 10 -4 = 0.00015 Just move the decimal back in the opposite direction

7. 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 = 6 + 4 = 17.16 10 1.716 x 10 11

8. 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 = 1.8 9 – 3 = 6 1.8 x 10 6

9. 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!!!

10. 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!!!

11. 10 -1 10 -2 10 -3 10 3 10 2 10 1 10 0 gLmgLm deci centi milli (d) (c) (m) kilo hecto deca (k) (h) (da) Units of Measurement (cont.) Ex 1. 250 g = kg Ex 2. 250 L = mL Ex 3. 250 hg = mg 0.250 250,000 25,000,000 2.5 x 10 -1 kg 2.5 x 10 5 mL 2.5 x 10 7 mg