Units and Measurement Physical Science Math and Units

Units and Measurement Physical Science

Math and Units n Math- the language of Physics n SI Units – International System ¨ MKS n. Length m n. Mass kg n. Time s n National Bureau of Standards n Prefixes

Base SI Units Symbol Quantity Unit Length meter m Mass kilogram kg Temperature kelvin K Time second s Amount of mole Substance Luminous Intensity candela mol Electric Current a ampere cd

Derived SI Units (examples) Quantity unit Symbol Volume cubic meter m 3 Density Speed kilograms per kg/m 3 cubic meter per second m/s Newton kg m/ s 2 N Energy Joule (kg m 2/s 2) J Pressure Pascal (kg/(ms 2) Pa

Limits of Measurement n Accuracy and Precision

Example: Evaluate whether the following are precise, accurate or both. Accurate Not Precise

n Accuracy - a measure of how close a measurement is to the true value of whatever is being measured.

Example: Accuracy n Who is more accurate when measuring a book that has a true length of 17. 0 cm? Susan: 17. 0 cm, 16. 0 cm, 18. 0 cm, 15. 0 cm Amy: 15. 5 cm, 15. 0 cm, 15. 2 cm, 15. 3 cm

n Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

Example: Precision Who is more precise when measuring the same 17. 0 cm book? Susan: 17. 0 cm, 16. 0 cm, 18. 0 cm, 15. 0 cm Amy: 15. 5 cm, 15. 0 cm, 15. 2 cm, 15. 3 cm

Significant Figures n The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.

Centimeters and Millimeters

SI Unit Prefixes Name gigamegakilodecicentimillimicronanopico- Symbol G M k d c m μ n p Analogy 109 106 103 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12

SI Unit Prefixes for Length Name gigameter megameter kilometer decimeter centimeter millimeter micrometer nanometer picometer Symbol Gm Mm km dm cm mm μm nm pm Analogy 109 106 103 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12

Scientific Notation Mx n. M n 10 is the coefficient 1<M<10 n 10 is the base n n is the exponent or power of 10

To write a number to scientific notation: 1)Put the decimal after the first nonzero digit. Example: To convert 5, 668, 000 first write 5. 668000

2) To find the exponent count the number of places from the decimal to the end of the original number. In 5. 668000 there are 6 places after the decimal. So the exponent is 6 or 106

3) Drop the ending (or beginning) zeros (if any). So 5, 668, 000 is written as: 5. 668 x 106

Scientific Notation n Exponents are often expressed using other notations. n 5. 668 E+6 n 5. 668 x 10^6 or

Numbers less than 1 will have a negative exponent. A millionth of a second is: 0. 000001 sec 1. 0 E-6 1 x 10 -6 1. 0^-6

Speed of Light n 300, 000 m/sec

Example 1 Express the following in scientific notation: 73, 822 m = 0. 001234 g = 34, 532. 666 s = 0. 447600 m =

Example 2 Express the following in standard numerical form: 4. 75 x 10 -3 m = 8. 99 x 107 g = 1. 44 x 101 s = 3. 334 x 10 -6 m =

Factor-Label Method of Unit Conversion n Example: Convert 5 km to m: NEW UNIT 5 km x 1, 000 m =5, 000 m km OLD UNIT

Factor-Label Method of Unit Conversion: Example n Example: Convert 7, 000 m to km 7, 000 m x 1 km =0. 007 m = 7 x 10 -3 km 1, 000 m

Problem Solving Method 1) Make a list of: knowns unknowns 2) a) If applicable, make a diagram. b) Write the related formula. c) Substitute the numbers with units and check that the units are uniform. 3) Write the answer with the units.

Multiplication in Scientific Notation n New coefficient= product of coefficients n New exponent= sum of exponents n Perform the following calculations: (9 x 105)m· ( 7 x 10 -6)m= (3 x 103)m· ( 2. x 103)m=

Division in Scientific Notation n New coefficient= quotient of coefficients New exponent= exponent of numerator -exponent of denominator n Perform the following calculations: 12 x 102 kg / 8 x 102 m 3= 24 x 104 kg/ 6 x 102 m 3=

Addition and Subtraction in Scientific Notation A. B. First express each number with the same exponent as the other New coefficient=sum of coefficients Perform the following calculations: 3 x 104 + 2 x 104= 5 x 1023 - 1. x 1022=