Basic Math Pre-assessment Review & Practice Problems Honors Environmental Science Ms. Sipe

Scientific Notation Scientific notation expresses very large or very small numbers as a multiple of 2 numbers; Based on powers of 10 Ex. 6 x The 1 st number The 2 nd number 1 ≤ X < 9 is 10 raised to a power The exponent is the # of places the decimal point must be shifted to give the regular or standard notation. + rt and - lf

Scientific Notation Examples Express the following in scientific notation = = 6022 = = Express the following in standard or expanded form 4.44 x = x 10 9 = 1.2 x = 1.8 x 10 2 =

Scientific Notation Answers Express the following in scientific notation = X = X = X = X Express the following in standard or expanded form 4.44 x = x 10 9 =7,121,000, x = x 10 2 =180

Scientific Notation Calculations To X exponential terms add the powers; to / exponential terms subtract. To + or – exponential terms, the exponents must be the same. Solve the following: a. (3.0 x )(6.0 x 10 2 ) = b. (2.0 x 10 4 ) ÷ (1.0 x )= c. (2.0 x 10 2 ) + (3.0 x 10 3 ) = d. (2.5 x 10 3 )(2.0 x ) = e. (7.0 x 10 1 ) = (3.5 x ) f. (5.5 x 10 3 ) - (5.0 x 10 2 ) =

Scientific Notation Calculations Answers To x exponential terms add the powers; to / exponential terms subtract. To + or – exponential terms, the exponents must be the same. Then, put the answer in proper scientific notation. Solve the following: a. (3.0 x )(6.0 x 10 2 ) = 1.8 X b. (2.0 x 10 4 ) ÷ (1.0 x )= 2.0 X c. (2.0 x 10 2 ) + (3.0 x 10 3 ) = 3.2 X 10 3 d. (2.5 x 10 3 )(2.0 x ) = 5.0 X e. (7.0 x 10 1 ) = 2.0 X 10 4 (3.5 x ) f. (5.5 x 10 3 ) - (5.0 x 10 2 ) = 5.0 X 10 3

SI - The international system of units Base Unit – need only one measurement Derived Unit – a combination of 2 or more base units Quantity Definitions Typical Unit SI Unit Base unit (B) or Derived unit (D) Equipment Mass Measure of the amount of matterggB Triple beam balance Volume Measure of the Space that matter takes up mL D Graduated cylinder Density ratio of the mass of an object to its volume. g/cm 3 or g/ml D Length distance between two points mmBRuler Time Duration of an eventssB Stop watch, clock, timer Temperature Measure of KE (vibration of molecules) °CKBthermometer

The Metric System and Prefixes X /

The Metric System and Prefixes METRIC CONVERSIONS USING DIMENSIONAL ANALYSIS: 1,000,000 µg = 1g1,000,000 µL = 1 L 1,000mg = 1 g1,000mL = 1 L 100cg = 1 g100cL = 1 L 10dg = 1 g 10dL = 1 L 1 kg = 1,000g 1 kL = 1,000 L Also should also know: Tera (T) Giga (G) 10 9 Mega (M) 10 6 Micro (u) Nano (n) Pico (p)

Metric Conversions milliliters to liters5) 11.7 grams to kilograms 2. 78,999 milligrams to grams6) kiloliters to liters centigrams to grams7) 44 centimeters to meters meters to millimeters 8) 277 kilograms to grams

Metric Conversion Answers milliliters to liters5) 11.7 grams to kilograms 876ml(1L/1000mL) = L11.7g (1 kg/1000g) = ,999 milligrams to grams6) kiloliters to liters 78,999mg(1g/1000mg) = g kL(1000L/1kL) =0.9 L centigrams to grams7) 44 centimeters to meters 0.9cg(1g/100cg)0.009 g 44cm(1m/100cm) = 0.44 m meters to millimeters 8) 277 kilograms to grams 112m(1000mm/1m) = 112,000 mL277kg(1000g/1kg)= 277,000 g

Dimensional Analysis What’s given? What do you want? Look for an equivalence statement to put into ratio form Show all work – Set-up (bridge) with all units – May have one or multiple steps Did you answer the question? Is the answer reasonable?

Dimensional Analysis Practice Given: 2.54 cm = 1 inch 1 mile = 5280 feet1 gallon = 4 quarts 3.79 L = 1 gallon 454 g = 1 pound 1 ft = 12 inches 16 ounces = 1 pound 1 calorie = 4.18 Joules 1 mL = 1 cm 3 1 L = 1000 mL1 mole = 6.02 X atoms Solve: 5.7 inches = _____________ cm85 ounces = ________________ lbs 125 grams = ______________ lbs72 cm 3 = ______________ mL 2.5 miles = ______________ feet4 moles = ________________ atoms

Dimensional Analysis Answers Solve: 5.7 inches = _____________ cm85 ounces = ________________ lbs 5.7in(2.54cm/1in) = cm85oz(1lb/160z) = 5.31lbs 125 grams = ______________ lbs72 cm 3 = ______________ mL 125g(1lb/454g) = 0.28lbs72 cm 3 (1mL/1cm 3 )= 72mL 2.5 miles = ______________ feet4 moles = ________________ atoms 2.5mi(5280ft/1mi)= 13200ft4mol(6.022X atoms/1mol)= 2.41 X atoms

More to Come: Nuclear Chemistry reactions & calculations. Concentration reactions & calculations