Basic MathPre-assessment Review &

Practice Problems

Honors Environmental ScienceMs. Sipe

Scientific NotationScientific notation expresses very large or very small numbers as a multiple of 2 numbers; Based on powers of 10

Ex. 6 x 1023

The 1st number The 2nd 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 ExamplesExpress the following in scientific notation0.2713 =314159 =6022 =0.12011 =

Express the following in standard or expanded form4.44 x 10-6 =7.121 x 109 =1.2 x 10-1 =1.8 x 102 =

Scientific Notation AnswersExpress the following in scientific notation0.2713 = 2.713 X 10-1

314159 = 3.14159 X 105

6022 = 6.022 X 103

0.12011 = 1.2011 X 10-1

Express the following in standard or expanded form4.44 x 10-6 = 0.000004447.121 x 109 = 7,121,000,0001.2 x 10-1 = 0.121.8 x 102 = 180

Scientific Notation CalculationsTo 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 10-8)(6.0 x 102) = b. (2.0 x 104) ÷ (1.0 x 1013)= c. (2.0 x 102) + (3.0 x 103) =d. (2.5 x 103)(2.0 x 10-7) = e. (7.0 x 101) = (3.5 x 10-3)f. (5.5 x 103) - (5.0 x 102) =

Scientific Notation Calculations AnswersTo 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 10-8)(6.0 x 102) = 1.8 X 10-5

b. (2.0 x 104) ÷ (1.0 x 1013)= 2.0 X 10-9

c. (2.0 x 102) + (3.0 x 103) = 3.2 X 103

d. (2.5 x 103)(2.0 x 10-7) = 5.0 X 10-4

e. (7.0 x 101) = 2.0 X 104

(3.5 x 10-3)f. (5.5 x 103) - (5.0 x 102) = 5.0 X 103

SI -The international system of units Base Unit – need only one measurement

Derived Unit – a combination of 2 or more base unitsQuantity Definitions Typical Unit SI Unit Base unit (B)

or Derived unit (D)

Equipment

Mass

Measure of the amount of matter g g B 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/cm3 or g/ml D

Length

distancebetween two points

m m B Ruler

Time

Duration of an event s s B Stop watch, clock, timer

Temperature

Measure of KE (vibration of molecules)

°C K B thermometer

The Metric System and Prefixes

103

102

101

100

10-1

10-2

10-3

X

/

The Metric System and Prefixes

METRIC CONVERSIONS USING DIMENSIONAL ANALYSIS:1,000,000 µg = 1g 1,000,000 µL = 1 L1,000mg = 1 g 1,000mL = 1 L100cg = 1 g 100cL = 1 L10dg = 1 g 10dL = 1 L1 kg = 1,000g 1 kL = 1,000 L

Also should also know:Tera (T) 1012

Giga (G) 109

Mega (M) 106

Micro (u) 10-6

Nano (n) 10-9

Pico (p) 10-12

Metric Conversions1. 876 milliliters to liters 5) 11.7 grams to kilograms

2. 78,999 milligrams to grams 6) 0.0009 kiloliters to liters 3. 0.9 centigrams to grams 7) 44 centimeters to meters

4. 112 meters to millimeters 8) 277 kilograms to grams

Metric Conversion Answers1. 876 milliliters to liters 5) 11.7 grams to kilograms 876ml(1L/1000mL) = 0.876 L 11.7g (1 kg/1000g) = 0.011700

2. 78,999 milligrams to grams 6) 0.0009 kiloliters to liters 78,999mg(1g/1000mg) = 78.999 g 0.0009kL(1000L/1kL) =0.9 L 3. 0.9 centigrams to grams 7) 44 centimeters to meters 0.9cg(1g/100cg)0.009 g 44cm(1m/100cm) = 0.44 m 4. 112 meters to millimeters 8) 277 kilograms to grams 112m(1000mm/1m) = 112,000 mL 277kg(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 PracticeGiven:2.54 cm = 1 inch 1 mile = 5280 feet 1 gallon = 4 quarts3.79 L = 1 gallon 454 g = 1 pound 1 ft = 12 inches16 ounces = 1 pound 1 calorie = 4.18 Joules 1 mL = 1 cm3 1 L = 1000 mL 1 mole = 6.02 X 1023 atoms

Solve:5.7 inches = _____________ cm 85 ounces = ________________ lbs125 grams = ______________ lbs 72 cm3 = ______________ mL 2.5 miles = ______________ feet 4 moles = ________________ atoms

Dimensional Analysis AnswersSolve:5.7 inches = _____________ cm 85 ounces = ________________ lbs5.7in(2.54cm/1in) = 14.478cm 85oz(1lb/160z) = 5.31lbs

125 grams = ______________ lbs 72 cm3 = ______________ mL 125g(1lb/454g) = 0.28lbs 72 cm3(1mL/1cm3)= 72mL

2.5 miles = ______________ feet 4 moles = ________________ atoms2.5mi(5280ft/1mi)= 13200ft 4mol(6.022X 1023 atoms/1mol)=

2.41 X 1024 atoms

More to Come:

Nuclear Chemistry reactions & calculations. Concentration reactions & calculations