Introduction to Physics: SI UNITS, METRIC PREFIXES, AND SCIENTIFIC NOTATION

Mathematics and Physics Physics is a branch of science that involves the study of the physical world: energy, matter, and how they are related. Physicists investigate the motions of electrons and rockets, the energy in sound waves and electric circuits, the structure of the proton and of the universe. The goal of this course is to help you understand the physical world.

Mathematics in Physics Physics uses mathematics as a powerful language. Equations can be used to model a phenomenon. Example: v = d/t Velocity (v measured in meters per second, v) is the quotient of Distance, ( d measured in meters, m) and Time (t, measured in seconds, s)

Example: Velocity The Velocity (v), the an object travels at equals the distance (d) divided by the time (t) that it take the object to travel that distance. That is, v (velocity) = d (distance) / t (time). What is the velocity of a car that travels a distance of 75m in a time of 3 seconds? Analyze the Equation…What happens to Velocity when distance d increases or time t increases?.....What happens to time t when distance d decreases?

Questions: What are the variables? What do the variables represent? What are the units for the variables? Example: v = x/t Variable Represent Unit v Velocity m/s (meters/second) d Displacement d (meters) t Time s (seconds)

Review of Basic SI Units In science laboratories, all measurements are recorded using metric or SI (Système International) units The standard SI unit for measuring mass is the gram. The abbreviation is ‘g’. The standard SI unit for measuring volume is the liter. The abbreviation is ‘l’ or ‘L’ The standard SI unit for measuring length is the meter. The abbreviation is ‘m’ The standard SI scale for measuring temperature is Celsius (or Centigrade). The abbreviation is oC The standard SI unit for time is the second abbreviated (s)

SI Units The worldwide scientific community and most countries currently use an adaptation of the metric system to state measurements. The Système International d’Unités, or SI, uses seven base quantities, which are below.

Metric Prefixes Chart Kilo (k) = 1000 or 103 hecto (h) = 100 or 102 unit (meter, liter, second, or gram) = 1 or 100 Metric Prefixes Chart deka (dk) = 10 or 101 Notice that each step on the line represents a change by a factor of 10. Larger than 1 unit deci (d) = 1/10, 0.1 or 10-1 centi (c) = 1/100, 0.01, or 10-2 milli (m) = 1/1000, .001, or 10-3 Smaller than 1 unit

An easy way to remember the prefixes! King - Kilo Henry- Hecto Died - Deka Unexpectedly - Unit Drinking - Deci Chocolate - Centi Milk- Milli Derived Units are combinations of base units. Ex. Kilogram, centiliter, millimeter

Prefixes used with SI Units To convert between SI units, multiply or divide by the appropriate power of 10. Prefixes are used to change SI units by powers of 10, as shown to the left.

Dimensional Analysis Dimensional analysis is used in choosing conversion factors. A conversion factor is a multiplier equal to 1. For example, because 1 kg = 1000 g, you can construct the following conversion factors:

1 min= 60 seconds 1 hour = 60 mins 1 hour = 3600 seconds Time Conversions 1 min= 60 seconds 1 hour = 60 mins 1 hour = 3600 seconds 1 day= 24 hours 1day = 86400 seconds 365 days = 1 year

What is Scientific Notation Scientific notation is a short-hand way of writing large numbers without writing all of the zeros. For example, 25,000 can be written as 2.5 x 104 There are 3 steps in converting a number into scientific notation. Step 1- Move the decimal point over till there is only one number in front of the decimal. Step 2- Write the number without zeros. Step 3- Count how many places you moved the decimal and make that your power of 10.

Precision vs. Accuracy Accuracy is the degree of closeness of a measured or calculated quantity to its actual (true) value Precision is the state of being precise or exact Ex. Think about throwing darts at a dart board. If you hit the bull’s eye, you are precise. If you hit somewhere on the dart board, you are accurate. The closer to the dartboard, the more accurate you are.

Significant Digits Suppose you use a meter-stick to measure a pen, and you find that the end of the pen is just past 14.3 cm. This measurement has three valid digits: two you are sure of, and one you estimated. The valid digits in a measurement are called significant digits. The last digit given for any measurement is the uncertain digit.

Rules for Significant Digits Leading zeros are never significant. 0.003 {1} Imbedded zeros are always significant. 5.00305 {6} Trailing zeros are significant only if the decimal point is specified. 30 (no) {1} , 30. (yes) {2} Hint: Change the number to scientific notation. It is easier to see. Addition or Subtraction: The answer has the same number of digits to the right of the decimal as that of the term with the least number of digits to the right of the decimal. The last digit retained is set by the first doubtful digit. Multiplication or Division: The answer has the same number of significant figures as that of the term with the least number of significant figures When rounding off numbers to a certain number of significant figures, do so to the nearest value. example: Round to 3 significant figures: 2.3467 x 104 (Answer: 2.35 x 104) example: Round to 2 significant figures: 1.612 x 103 (Answer: 1.6 x 103) What happens if there is a 5? There is an arbitrary rule: If the number before the 5 is odd, round up. If the number before the 5 is even, let it be.

Given a set of data how does one create a graph and analyze it. Graphing Given a set of data how does one create a graph and analyze it. A well designed graph is more than “a picture worth a thousand words”. It can give you more information than words. To be useful, it must be drawn properly.

Graphing

Drawing your best-fit line

1 min= 60 seconds 1 hour = 60 mins 1 hour = 3600 seconds Time Conversions 1 min= 60 seconds 1 hour = 60 mins 1 hour = 3600 seconds 1 day= 24 hours 1day = 86400 seconds 365 days = 1 year