apes calculations without calculators. 1.use exponents whenever numbers are especially large or...
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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
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
Helpful energy info
W= watt=1kW=kilowatt= 1 thousand WMW= megawatt= 1 million WGW=gig watt= 1 billion W