REALLY, REALLY SMALL NUMBERS. Scientific Notation A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS.

Rules for Scientific Notation To be in proper scientific notation the number must be written with a number between 1 and 10 and multiplied by a power of ten 23 x 105 is not in proper scientific notation. Why?

137,000,000 can be rewritten as 1.37 X 108

Using scientific notation, rewrite the following numbers. 347,000. 3.47 X 105 902,000,000. 9.02 X 108 61,400. 6.14 X 104

Negative Exponents = 10-1 = = 10-2 = = 10-3 = = 10-4

A ribosome, a part of a cell, is about 0 A ribosome, a part of a cell, is about 0.000000003 of a meter in diameter. Write the length in scientific notation. 3 x 10-9 m

Metric Prefixes

Common Prefixes Prefix Symbol Multiplier Kilo k 103 1,000 Centi c 10-2 .01 Milli m 10-3 .001 Micro μ 10-6 .000001 Nano n 10-9 .000000001

Examples How many mm in a Meter? How many μg in a Gram? How many ns in a Second? 109ns How many km in a Meter? 10-3km

SI Units Fundamental Quantities Length = Meters (m) Mass = Kilograms (Kg) Time = Seconds (s) Found through direct measurement Building blocks for the SI measurement system. Is Volume a fundamental Quantity?

Base vs. Derived Units Derived Units are constructed through combinations of base units Usually base units multiplied/divided to develop these Derived units supported by physics formulas Velocity (rate) = Distance / Time so velocity units = m / s

Metric Conversions

The Factor label Method A way to solve math problems in physics Used to convert km to miles, m to km, N to g, g to N, etc. To use this we need: 1) desired quantity 2) given quantity 3) conversion factors Conversion factors are valid relationships or equalities expressed as a fraction and equal to one!

Equalities length 10.0 in. 25.4 cm State the same measurement in two different units length 10.0 in. 25.4 cm

Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units but always equal to one. You can always multiply any equation by this equality and not change the quantity, just the units. Example: 1 in. = 2.54 cm Factors: 1in. and 2.54 cm 2.54 cm 1 in.

Write conversion factors for 1 foot = 12 inches For example: 1 km = 0.6 miles the conversion factor is Write conversion factors for 1 foot = 12 inches What conversion factors can you think of that involve meters?

Conversion Factors Conversion factors for 1 ft = 12 in There are almost an infinite number of conversion factors that include meters:

Factor label Example First write down the desired quantity How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) First write down the desired quantity Write down given quantity Write down all conversion factors

More Examples # Can$ = 100.00 US$ x 1 Can$ 0.65 US$ = 153.85 Can$ 1. You want to convert 100.00 U.S. dollars to Canadian dollars. If the exchange rate is 1 Can$ = 0.65 US$, how much will it cost? # Can$ = 100.00 US$ x 1 Can$ 0.65 US$ = 153.85 Can$

Learning Check Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 1 Liter = 1000 mL 2. hours and minutes 1 hour = 60 minutes 3. meters and kilometers 1000 meters = 1 kilometer

How many minutes are in 2.5 hours? 2.5 hr x 60 min = 150 min 1 hr By using dimensional analysis/factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!