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  6.5 x  5.43 x 10 -4

Practice 1.1,000,000,000, X x10 -4

Helpful scientific notation # of zerosScientific notation 3Thousand10 3 6Million10 6 9Billion trillion10 12

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 ) – (1.5 x ) (19 x ) - (1.5 x ) = 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 10 5 ) (4.5 x 10 5 ) = x When dividing numbers, the exponents are subtracted, numerator exponent minus denominator exponent. Example: 9 x 10 5 = 3 x x 10 3

US consumes 20 million barrels of oil per day Estimated 10 billion barrels of recoverable oil on the refuge 1. 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 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 OR old unit x new unit = new unit 1 old unit Example: 25 ft x 1 yd x m = meters 3 ft 1 yd

Be sure to know how to convert numbers to percentages and percent change. Be sure to know how to convert numbers to percentages and percent change. Example: If 200 households in a town of 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! Show all of your units, too! Numbers given without units are often not counted even if correct.

Helpful energy info W= watt=1 kW=kilowatt= 1 thousand W MW= megawatt= 1 million W GW=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 1ft2 1 pound of coal produces 5,000 BTU’s