Scientific Notation Scientific Notation and Units of and Units of

MeasurementMeasurement

Scientific NotationScientific Notation

Scientists often deal with both very Scientists often deal with both very large and very small numbers.large and very small numbers.

Ex. 0.00000000000000001 or 100,000,000,000,000,000Ex. 0.00000000000000001 or 100,000,000,000,000,000

To keep things simple, we express To keep things simple, we express these numbers as powers of 10.these numbers as powers of 10.

Scientific NotationScientific Notation

Scientific Notation Scientific Notation (cont.)(cont.)

Scientific notation is expressed as:Scientific notation is expressed as:

M x 10M x 10ªª

Any number between 1 & 10

Power of 10

“a” determines the number of powers

Scientific Notation Scientific Notation (cont.)(cont.)

Example 1. 2500000 0= 2.5 x 102.5 x 1066

Example 2. 000005 = 5 x 105 x 10-5-5

Decimal behind # = right to left = positive 10 power

Decimal in front of # = left to Right = negative 10 power

Class Practice:Class Practice:

1. Convert 1. Convert 31,00031,000 to scientific notation. to scientific notation.

2.Convert 2.Convert 0.000120.00012 to scientific notation. to scientific notation.

Scientific Notation Scientific Notation (cont.)(cont.)

3.1 x 3.1 x 101044

1.2 x 101.2 x 10--

44

You can also convert scientific You can also convert scientific notation back to standard notation.notation back to standard notation.

Scientific Notation Scientific Notation (cont.)(cont.)

Example 1. Example 1. 1.4 x 101.4 x 105 5 == 140,000140,000

Example 2. Example 2. 1.5 x 101.5 x 10-4-4 = = 0.000150.00015

Just move the decimal back in the opposite direction

Multiplying numbers in scientific Multiplying numbers in scientific notation:notation:

Scientific Notation Scientific Notation (cont.)(cont.)

(4.4 x 10(4.4 x 1066) x (3.9 x 10) x (3.9 x 1044) =) =

4.4 x 3.9 4.4 x 3.9 == 6 + 4 =6 + 4 =

17.1617.16

1010

1.716 x 101.716 x 101111

Dividing numbers in scientific notation:Dividing numbers in scientific notation:

Scientific Notation Scientific Notation (cont.)(cont.)

(5.76 x 10(5.76 x 1099) ) ÷÷ (3.2 x 10 (3.2 x 1033) =) =

5.76 5.76 ÷ 3.2 =÷ 3.2 = 1.81.8

9 – 3 =9 – 3 = 66

1.8 x 101.8 x 1066

Units of MeasurementUnits of Measurement

2 systems of measurement in use2 systems of measurement in use

English English ( yards, gallons, miles, feet)( yards, gallons, miles, feet)

Metric Metric (meters, liters, kilometers)(meters, liters, kilometers)

Scientists use this system!!!

Why is it important that we know Why is it important that we know what system we are using?what system we are using?

Units of Measurement Units of Measurement (cont.)(cont.)

MARS

STOP

SPLAT

NASA orbiter (1999): 125 million dollar conversion error!!!

10-1 10-2 10-3103 102

101

100

g

L

m

deci centi milli

(d) (c) (m)

kilo hecto deca

(k) (h) (da)

Units of Measurement Units of Measurement (cont.)(cont.)

Ex 1. 250 g = kg

Ex 2. 250 L = mL

Ex 3. 250 hg = mg

0.250.2500250,00250,000025,000,0025,000,0000

2.5 x 10-1 kg

2.5 x 105 mL

2.5 x 107 mg