Scientific Notation and Units of Measurement

1. Scientific Notation and Units of Measurement

2. Scientific Notation • 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. Scientific Notation

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

4. Scientific Notation (cont.) Decimal behind # = right to left = positive 10 power Example 1.2500000 0= 2.5 x 106 Decimal in front of # = left to Right = negative 10 power Example 2.000005 = 5 x 10-5

5. Scientific Notation (cont.) Class Practice: 1. Convert 31,000 to scientific notation. 2.Convert 0.00012 to scientific notation. 3.1 x 104 1.2 x 10-4

6. Scientific Notation (cont.) • You can also convert scientific notation back to standard notation. Just move the decimal back in the opposite direction 140,000 Example 1. 1.4 x 105 = Example 2. 1.5 x 10-4 = 0.00015

7. Scientific Notation (cont.) • Multiplying numbers in scientific notation: 1.716 x 1011 (4.4 x 106) x (3.9 x 104) = 4.4 x 3.9 = 17.16 6 + 4 = 10

8. Scientific Notation (cont.) • Dividing numbers in scientific notation: (5.76 x 109) ÷ (3.2 x 103) = 1.8 x 106 5.76 ÷ 3.2 = 1.8 9 – 3 = 6

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

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

11. kilo hecto deca (k) (h) (da) deci centi milli (d) (c) (m) g L m 2.5 x 10-1 kg 103 102 101 10-1 10-2 10-3 2.5 x 105 mL 2.5 x 107 mg 100 Units of Measurement (cont.) Ex 1. 250 g = kg 0.250 Ex 2. 250 L = mL 250,000 Ex 3. 250 hg = mg 25,000,000