Math Skills In this chapter we will review basic skills necessary to perform mathematical calculations in physics, these include Signed Numbers Metric System conversions Significant Figures Scientific Notation

Signed Numbers Addition Rule: To add two numbers of like sign, we add the absolute values of the numbers and give the sum the common sign. To add two numbers of unlike sign, we find the difference of their absolute values and give the result the sign of the larger value. (+6) + (+2) = +8 (+6) + (-2) = + 4

Signed Numbers To subtract one signed number b from another signed number a, we change the sign of b and then add it to a, using the addition rule. (+8) - (+5) = 3 (-8) – (+5) = -13

Signed Numbers Multiplication Rule: If two factors have like signs, their product is positive. If two factors have unlike signs, their product is negative (+2)(+3) = +6 (-3)(-4) = +12 (-2)(+3) = -6 (-3) (+4) = -12

Signed Numbers Division Rule: The quotient of two numbers of like sign is positive, and the quotient of two numbers of unlike sign is negative. (+2) ÷ (+2) = +1 (-4) ÷(-2) = +2 (+4)÷ (-2) = -2 (-4) ÷ (+2) = -2

Quadratic Equations For mathematical expressions involving a second order term, arrange the equation to identify a, b, and c. ax2 + bx + c = 0 Two solutions will be obtained from the quadratic equation

Metric System The Metric System is a set of standards that is widely adopted to make measurements meaningful We will consider standards for length, time, and mass

Metric System The mass standard is a platinum/iridium cylinder kept under vacuum.

Metric System The atomic clock is based on vibrations of the Cesium atom. One second is the time needed for 9,192,631,770 vibrations of the Cesium atom.

Metric System The standard of length is based on the distance light travels in a certain period of time. One meter is the length of path traveled in a vacuum in a time interval of 1/299,792,458 seconds.

Metric System Prefixes Prefix Multiple Symbol PrefixMultipleSymbol Pico p Nano10 -9 n micro10 -6 µ milli10 -3 m centi10 -2 c Kilo10 3 K Mega10 6 M Giga10 9 G

Derived Units Derived units are mathematical combinations of the basic units. Example #1 velocity: meters/second Velocity has units of length/ time Example #2: area: meters 2 Area is length x length

Significant Figures The following are always significant: All nonzero digits All zeroes between nonzero digits Zeroes to the right of an non-zero digit and left of a written decimal point Zeroes to the right of a non-zero digit and right of a written decimal point The following are never significant Zeroes to the right of a nonzero digit, but to the left of an unwritten decimal point Zeroes to the left of the decimal point in numbers less than one. Zeroes to the right of a decimal point, but to the left of the first non-zero digit

Adding Significant Figures When adding or subtracting using significant figures- express your answer to the same digit as the least accurate term. Examples = =

Multiplying and Dividing Significant Figures Complete the operation your problem specifies. Count the number of significant figures in each term. The answer is expressed to the smallest number of significant figures in any term. Examples 1.4 x = 618/50 =

Scientific Notation Scientific Notation is a shorthand used to express large and small numbers. In scientific notation we our value as a number between 1 and 10 times an integral power of becomes 2.1 x ,450,000 becomes 3.45 x 10 6

Arithmetic Operations in Scientific Notation Adding and subtracting with like exponents 4 x x 10 8 = Adding and subtracting unlike exponents 4.0 x X10 5 = Multiplication (3 x 10 6 m) (2 x 10 3 m) = Division 8 x 10 6 m/ 2 x10 3 s =