APES Intro Math Practice! Place the following numbers into scientific notation. No Calculators!! 1) one billion 2) twenty three thousand 3)

Perform the following calculations in scientific notation. No Calculators!! five hundred billion times thirty five thousand six thousand divided by 300 billion

Metric Conversions—All APES students should be comfortable converting between common metric prefixes. Below are common prefixes, and the number of base units each represents. For example, 1 teraWatt = 10 9 Watts; 1 millimeter = meters n = nano =  = micro = m = milli = k = kilo = 10 3 M = mega= 10 6 T = Tera = 10 9 G = Giga = 10 12

2.8 mm = ____________ m 1.3 nm = ____________ mm 300 mg = ____________g

Unit conversions—All APES students should be able to convert from one system of units to another. Use the information below to complete the following. Show all of your work including the canceling of all units. No Calculators!! 1 mi 2 = 640 acres1 acre = hectares 1 barrel oil = 42 gallons1 L = gallons 1 kilowatt-hour = 3.4 x 10 4 BTU= 8.6 x 10 5 calories 1 metric ton (tonne) = 1 x 10 3 kg 12) A 100 square mile area of national forest is how many acres? how many hectares?

Fifty eight thousand kilograms of solid waste is equivalent to how many metric tons?

A city that uses ten billion BTUs of energy each month is using how many kilowatt-hours of energy?

Percentages—All APES students should be able to work comfortably with percentages. If the concentration of mercury in a water supply changes from 65 parts per million (ppm) to 7 ppm in a ten-year period, what is the percentage change of the mercury concentration? How much per year?

A natural gas power plant is 60% efficient. If one cubic meter of natural gas provides 1000 BTUs of electricity. How many BTUs of waste heat were produced? If 35% of a natural area is to be developed, leaving 500 acres untouched, how many acres are to be developed?

Dimensional Analysis practice Olive oil has a density of 7.64 lbs/gallon. What is its density in grams/mL? 1 qt = 0.95 L 4 qt = 1 gal 1 lb = 454 g

Start with given density. Set up conversion ratios that allow you to cancel original unit (lb/gallon) to the desired unit (g/mL). (Can start with either the mass conversion or the volume conversion) 7.64 lb x 1 gal x 1 qt x 1 L x 454 g gal 4 qt 0.95 L 1000 mL 1 lb = 0.91 g/mL

Practice Examples How many cm are there in 6 feet? (1 inch = 2.54 cm) Traveling at 65 miles/hour, how many feet can you travel in 22 minutes? (1 mile = 5280 feet)