Math Techniques for

AP Physics

Scientific Notation

A valuable way to express large and small numbers

A useful way to communicate the number of significant figures in a numerical value

Mt. Everest -- 8845 m or 8.845 x 103 m

Flu Virus -- 0.00000023 m or 2.3 x 10-7 m

Rules for Scientific Notation

• Decimal is moved so that one significant digit precedes it

• Numbers are expressed as a value multiplied by a power of 10

1230 23405

Rules for Scientific Notation

• When the decimal is moved to the right, the exponent is negative. When the decimal is moved left, the exponent is positive.

8463 0.00543 0.00000054020

Metric SystemWidely used system of measurement because of its ease of use

Base units are expressed with prefixes representing various powers of ten

SI (Systeme International) Units

• the internationally agreed upon standard units for the metric system

• Base SI units are:

Kilogram – mass

Meter – length

Second – time

Ampere – electric current

Other metric units derived from base units:

Newton -- kg x m/s2 (force) Joule -- kg x m2/s2 (energy) Volt -- kg x m2/(A x s3) (electric potential) Tesla -- kg/(A x s2) (magnetic induction)

Converting metric to metric:

250 cm = __________ m

45 kg = ___________ g

Metric Prefixes

Unit Conversion

To change a measured value from one unit to another, you need a conversion factor.

21.5 inches = _______ cm

1 inch = 2.54 cm

Think of that factor as a fraction. The conversion factor will be set up so that the original units cancel out to give you the new units

The 14 tallest peaks in the world are referred to as “eight-thousanders,” meaning the summits are 8000. m above sea level. What is the elevation, in feet, of an elevation of 8000. m?

m cm inches feet

A silicon chip has an area of 1.25 square inches. Express this area in square centimeters.

1 in = 2.54 cm

1 in2 = ______ cm2

Where the posted speed limit is 55 miles per hour, what is the speed in meters per second?

mi/hr mi/s ft/s in/s cm/s m/s