Math Review

What not to do:

Basic Terms Width Hypoteneuse Height Height Length Base Right Angle

Basic Terms Width Hypotenuse Height Height Length Base Right Angle Area of a Side= (length)(width) or (length)(height) or (height)(width) Volume of Rectangle= (length)(width)(height) Area=1/2 (Base)(Height)

Basic Units Length – meter (m) Mass – gram (g) Time – second (s) Volume – liter (L) Prefixes: Kilo (k) = x1000 Centi (c) = /100 Milli (m) = /1000

Basic Units of Measurement Quantity Name Symbol SI Base Unit Derived Unit Length Meter m - Area Square Meters A m2 Volume Cubic Meters V M3 Velocity Meters per second ν m/s Acceleration Meters per second squared a m/s2 Force Newton N Kg m/s2 J/m Energy Joule J Kg m2/s2 N m Mass Gram g Power Watt W Kg m2/s3 J/s

Metric English Equivalents 1 meter 39 inches 2.54 cm 1 in 1 kg 2.21 lbs 454 g 1 lb 1 liter 1.057 quarts 28.4 g 1 oz. 16.5 cm3 1 in3 3.78 L 1 gallon

Significant Figures Two Rules: If there is NO decimal point – start at the RIGHT and count, beginning with the first non-zero digit. Ex. 340 2 sig figs 30400 3 sig figs 34955 5 sig figs If there IS a decimal point – start at the LEFT and count, beginning with the first non-zero digit. Ex. 340. 3 sig figs 30400 5 sig figs 0.34955 5 sig figs 0.00040 2 sig figs

Practice Sig Figs How many sig figs in each number? A) 921 B) 92100 C) 92100. D) 0.000210 E) 0.00219 F) 93,000,000 G) 93,000,003 H) 93,000,000. I) 20.09

Operations with Sig Figs Rule: Count the number of sig figs in each number you are multiplying or dividing. Use all numbers you have in calculations. The round answer to lowest number of sig figs in problem. Ex. 28.33 x 3.12 = 88.3896 calculator answer 4 s.f. 3 s.f. 6 s.f. So round to 3 s.f. Answer is 88.4 Ex. 28.44 / 3.12 = 9.08012805 calculator answer 4 s.f. 3 s.f. 6 s.f. So round to 3 s.f. Answer is 9.08

More Operations with Sig Figs Rule: When adding or subtracting, the answer should have the same number of decimal places as that of the number with the least decimal. Ex. 4.838 486.588 + 1.0023 - 421.00 5.3853 65.588 is 0-4, so is 5-9 , so round down round up = 5.385 =65.59 Remember: Decimal points must line up!

More Sig Fig Practice 0.00000313 78 +17 - .99 0.00000313 78 +17 - .99 4.9670 336,000-33,000.03= -3.1 0.000343 0.99 - .1 = - 17

Scientific Notation Use to express really Big and really small numbers. Rules: Only ONE digit to the left of the decimal X10 to however many places you had to move the decimal point. If you moved the decimal to the left, the power to positive If you moved the decimal to the right, the power is negative

Practice with Sci. Not. Put in Sci. Not: Put in regular numbers: 24327= 4.82 x 102= 73.54= 7.8 x 104= 0.00453= 1.2 x 10-4= 1.0067= 9.01 x 10-2=

Add/Subtract with Sci Not The exponents must be the same. Do what you need to do change one of the numbers to the other’s exponent. Then add/subtract the base numbers together and keep the exponent. Ex: 4.55 x 102 + 3.77 x 103 = ? Change 4.55 x 102 to 0.455 x 103 Then add 0.455 + 3.77 = 4.225 Add in x 103 And the answer is 4.225 x 103

Multiply/Divide with Sci Not First multiply/divide the base numbers together. Then for multiplication, add the exponents together. For division, subtract the exponents. Ex. (2.4 x 102)x(3.2x 103) 2.4 x 3.2 = 7.68 Add the exponents – 2 + 3 = 5 Giving the answer: 7.68 x 105 If we were dividing: 2.4/3.2 = 0.75 Subtract exponents – 2 – 3 = -1 Answer: 0.75 x 10-1 (You would then move the decimal point to leave one digit to the left for 7.5 x 100 or just 7.5.)

Metric Conversions Standard unit of distance is the meter. It is abbreviated m. For very small things, it may be more appropriate to use centimeters or even millimeters: 1m = 100 centimeters (cm) 1cm = 10 millimeters (mm) How many millimeters are in 1m? For very large distances, it may be more appropriate to use kilometers: 1kilometer (km) = 1000m What would you measure with km? cm? mm? m?

Metric Conversions Standard unit of mass is the gram. It is abbreviated g. For small amounts, you may want to use the milligram (mg) which is 1/1000th of a gram. For large amounts, you may want to use the kilogram (kg) which is 1000g. What would you want to measure in mg? Kg? g?

Solving for variables Always do the same thing to both sides of the equation and you will be fine. Ex. Density = mass/volume Solve for mass. Solve for volume. Ex. E = mc2 Solve for c. Ex. A + B = C A + C = D Solve for C.

Dimensional Analysis (or Canceling out) To convert from one type of unit to another type, we use dimensional analysis. For example, if we want to convert 55mph to km/h we just need to set the problem up correctly. 55 miles x 5280 ft x 39 cm x 1 m x 1 km = 1 hour 1 mile 3 ft 100 cm 1000 m 38 km = 38 kph 1 hour