Scientific notation (exponential notation) Used primarily in working with large or small numbers These numbers often have lower numbers of significant digits General form is M x 10n Where 10 > M ≥ 1 and n is any positive or negative integer Scientific notation has the decimal placed in standard form – to the right of the first nonzero digit

Examples of expansions 5.14 x 105 mm = 514,000 mm 3.45 x 10-4 kg = 0.000 345 kg Recognize, if the power of ten is positive, the number ‘s value must be greater than 1 AND If the power of ten is negative, the number’s value must be less than 1

Moving the Decimal Shifting the decimal to the left increases the power of ten in a positive manner 3.4 x 103 ft = 0.034 x 105 ft Shifting the decimal to the right increases the power of ten in a negative manner 3.4 x 103 ft = 34 x 102 ft

Returning to 100 Shifting the decimal to the left increases the power of ten in a positive manner 3.4 x 103 ft = 3,400 ft Shifting the decimal to the right increases the power of ten in a negative manner 3.4 x 10-3 ft = 0.003 4 ft

Adding in Scientific Notation All terms must have the same power of ten If any terms have different powers of ten, temporarily shift the decimal to obtain like powers Once all terms have the same power of ten, add the coefficient terms, round off for significant figures, retain the power of ten. IF NECESSARY, put in standard form!!

Subtracting in Scientific Notation All terms must have the same power of ten If any terms have different powers of ten, temporarily shift the decimal to obtain like powers Once all terms have the same power of ten, subtract the coefficient terms, round off for significant figures, retain the power of ten. IF NECESSARY, put in standard form!!

Multiplying in Scientific Notation Multiply the coefficient terms of all factors Sum the powers of ten for all factors Round for significant figures as needed Correct for standard scientific notation form

Example e.g. 1.23 x 103 m x 7.3 x 102 m = 8.979 x 105 m2 Proper form = 9.0 x 105 m2 e.g. 4.5 x 105 kg x 3.6 x 103 m/s2 = 16.2 x 108 kg-m/s2 = 16 x 108 kg-m/s2 Proper form = 1.6 x 109 kg-m/s2

Division in Scientific Notation Divide the numerator or dividend coefficient by the denominator or divisor coefficient Subtract the power of ten of the denominator or divisor from the power of ten of the numerator or dividend Round off for significant figures Correct for standard scientific notation form

Scientific Notation & Powers of Exponentials: The digit term is raised to the indicated power and the exponent is multiplied by the number that indicates the power. e.g. (2.4 x 104 m)3 = (2.4)3 x 10(4x3) m3 = 13.824 x 1012 m3 Proper form = 1.4 x 1013 m3 (to 2 significant figures)

When to Use Scientific Notation this Year? I am anticipating scientific notation to be used for numbers with a value of 10,000 or greater and for numbers with a value of a 0.000 1or smaller. Also, scientific notation is just another means for expressing a numerical value, therefore, SIGNIFICANCE does not change when moving into or out of scientific notation form!!!

A quantity is represented by a number and a unit Measurement A quantity is represented by a number and a unit The unit in a quantity and hence science is extremely important. It provides the standard to which our measurement is compared

SI SYSTEM The SI system is based primarily upon the metric system The SI system employs prefixes in order to express quantities reasonably based upon their magnitude

SI Prefixes Prefix Symbol Value Power of 10 mega- M 1,000,000 10+6 Prefixes with values greater than one. Prefix Symbol Value Power of 10 mega- M 1,000,000 10+6 kilo- k 1,000 10+3 hecto- h 100 10+2 deka-/deca- dk/da 10 10+1

SI Prefixes Prefixes with value less than one Prefix Symbol Value Power of 10 deci- d 0.1 10-1 centi- c 0.01 10-2 milli- m 0.001 10-3 micro- μ 0.000 001 10-6 nano- n 0.000 000 001 10-9 pico- p 0.000 000 000 001 10-12

Length distance covered by a line segment connecting two points SI standard unit is the meter, symbol “m” English to metric equivalent [ 1 inch = 2.54 cm ]

Volume (capacity) - Useful equalities are: 1 L = 1 dm3 and amount of space defined by three dimensions SI standard unit of measurement is the m3 the liter is an older metric unit of volume that is frequently employed today - symbol L - Useful equalities are: 1 L = 1 dm3 and 1 mL = 1 cm3 English to metric equivalent is: 1.056 688 quarts = 1 L L = 1.056 qts.

Do you know? What are formulas to determine the volume of a: cube, rectangular solid, cylinder, sphere, etc.? What are equalities for the units: - 1 bushel = 4 pecks - 1 peck = 8 dry quarts - 1 dry quart = 2 dry pints

Do you know? Liquid measure: - 1 gallon = - 1 quart = - 1 pint = - 1 cup = Units of length cubed: - 1 yard3 = - 1 foot3 = - 1 cord =

Area Measurement of a surface as defined by two dimensions SI standard is the m2

Area What are formulas to find the area of a: square, rectangle, triangle, circle, etc.? What are equalities for the units: - 1 mi2 = - 1 acre = - 1 ft2 = - 1 yd2 =

Mass Measurement of a quantity of matter Matter is anything having mass and volume OR anything exhibiting inertia Mass is a measure of inertia Inertia? Standard SI unit is the kilogram, kg

Weight The measurement of force acting on a mass Common field of force is gravity Gravity is – SI standard unit is – Newton (N) 1 N = 1 kg m / s2

Weight English (U.S.) - poundals - a unit of force equal to that required to give a mass of one pound an acceleration of one foot per second per second - 1 poundal = 0.138 N

Weight - 1 pound force = 4.448 N - 1 pound (Lb.) = 4.448 N Pounds-force The pound-force is equal to a mass of one avoirdupois pound multiplied by the standard acceleration due to gravity on Earth, which is defined as exactly 9.80665 meter per second squared - 1 pound force = 4.448 N - 1 pound (Lb.) = 4.448 N

Mass Why is mass preferred over weight? English to metric equality 1 Lb. = 453.592 37 grams USE: 1 Lb. = 453.6 g

Time Time is the measured interval between two occurrences or events SI standard unit is the second, s

Derived Units Fundamental or base units are obtained from making one measurement. If two or more measurements and hence their units are combined, the resulting unit is referred to as a derived unit. e.g. m3 , g/cm3, ft. /sec , Lbs./in2

Dimensional Analysis Dimensional analysis or factor label is a problem solving method that places an emphasis upon the accountability of units One of its primary functions is unit conversions The process involves multiplying a “given” by one or more conversion factors in order to change the units of the quantity without changing the magnitude of the quantity

Conversion Factors Conversion factors are ratios (fractions) with a value of one (1) These factors may be obtained from equalities or from other “given” pieces of information This process enables one to use COMMON pieces of information in the problem solving process

Performing Dimensional Analysis Start with the “ given” upon which the “find” will depend This “given” is often placed over one (1) to emphasize its numerator position Logically, multiply this “given” by ordered conversion factor(s) that will cancel out undesired units and introduce desired units Continue multiplying by conversion factor(s) until the final desired unit is obtained

How to use SI prefixes? Recommendation: Place the coefficient of one in front of the prefixed unit, set an equals sign, the power of ten representing the prefix, and then the base unit. 1 prefixed unit = power of ten base unit 1 kilometer = 10+3 m

More SI prefix information When converting between two SI units, the conversion may be performed in: 1)Two steps by converting to the base and then to the desired unit 2) In one step by applying a single conversion factor between the units - why did we select metric?

Example 5 mg to kg k - 10+3 Δ = 10+/-6 m – 10-3 10+3 – (-3) = 10+6 10-3 – (+3) = 10-6

Example continued Recall 1 large unit equals many small units 1 large unit = 10+? smaller units Recall 1 small unit equals a fraction of the large unit 1 smaller unit = 10-? larger units