APES calculations without calculators

1. Use exponents whenever numbers are especially large or small.

Scientific notation is a way to express, numbers the form of exponents as the product of a number (between 1 and 10) and raised to a power of 10.

650 000 6.5 x 105

0.000543 5.43 x 10-4

Practice

1. 1,000,000,000,0002. 87183. 2.223 X 109

4. 0.000000078325. 4.444 x10-4

Helpful scientific notation# of zeros Scientific notation

3 Thousand 103

6 Million 106

9 Billion 109

12 trillion 1012

When adding or subtracting numbers with exponents the exponents of each number must be the same before you can do the operation.

Example: (1.9 x 10-3) – (1.5 x 10-4 ) (19 x 10-4 ) - (1.5 x 10-4 ) = 17.5 x 10-4

When multiplying numbers with base 10 exponents, multiply the first factors, and then add the exponents.

Example, (3.1 x 105) (4.5 x 105) =13.95 x 1010

When dividing numbers, the exponents are subtracted, numerator exponent minus denominator exponent.

Example: 9 x 10 5 = 3 x 10 2

3 x 10 3

• US consumes 20 million barrels of oil per day• Estimated 10 billion barrels of recoverable oil

on the refuge1. How many days would the technically

recoverable oil resources on the refuge supply the total US demand for oil?

Use Dimensional Analysis or factor/label method for calculations

The following formula based on the cancellation of units is useful:

Given Value x Conversion factor =Answer 1

ORold unit x new unit = new unit

1 old unitExample:

25 ft x 1 yd x 1.094 m = 9.117 meters 3 ft 1 yd

Be sure to know how to convert numbers to percentages and percent change.

Example: If 200 households in a town of 10000 have solar power, what percent does this represent?

200/10000 x 100%= 2

Show ALL of your work and steps of calculations, even if they are too simple.

Show all of your units, too!

Numbers given without units are often not counted even if correct.

Helpful energy info

W= watt=1kW=kilowatt= 1 thousand WMW= megawatt= 1 million WGW=gig watt= 1 billion W

We want to determine the amount of coal needed to heat a 500 ft2 room. Need to know it takes 200 BTU’s to heat 1ft21 pound of coal produces 5,000 BTU’s