Energy Flow in Technological Systems Math Background

Units International system of units Ways of measurement Most calculations in science carry some sort of units, such as meters, volts, seconds or calories. We are interested in managing these units, not just to make our calculations mean something, but also as a very useful guide to how to do the calculation. Provides accuracy of data m- meter (distance-d) m/s- meter per second (average speed-v) s- seconds (time-t)

Conversions identify the unknown, including units Identify whether you will want a bigger or smaller number multiply starting measurement by conversion factors check the result: does the answer make sense? Should the new measurement be bigger or smaller than the starting number

Significant Digits Also called significant figures and abbreviated sig figs, sign.figs, sig digs or s.f. When working with number quantities in the sciences, particularly in Physics and Chemistry, it is important to follow the conventions about how to round answers. In order to do this correctly, you have to know how many digits in a number are significant. Significant figures are important because they tell us how good the data we are using are.

Why Sig Digs 100 grams 100. grams grams 100 grams This measurement is only accurate to the nearest 100 grams (i.e. the value of what we’re measuring is closer to 100 grams than it is to 200 grams or 0 grams) grams Because the last significant figure is in the “ones” place, the measurement is accurate to the nearest gram (i.e. the value of what we’re measuring is closer to 100 grams than it is to 101 grams or 99 grams) grams The third number has five significant figures (as we’ll talk about later). Because the last significant figure is in the “hundredths” place, the measurement can be considered to be accurate to the nearest 0.01 grams (i.e. the value of what we’re measuring is closer to grams than it is to or grams).

Scientific Notation Shorter method to express very large numbers. Based on powers of the base number ,000,000,000 in scientific notation is written as 1.23 x The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10. The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x the number 11 is referred to as the exponent or power of ten.

Solving for unknown variable At all times remember two basic rules from math... 1.To move something to the other side, just do the opposite math operation to it. 2.If you do it to one side, do it to the other.

Scalar vs. Vector Scalars are quantities that describe size or amount (magnitude) for example speed, distance, time Distance is a scalar describing the length between 2 points or locations (d)

Vectors Vectors are quantities that describe direction as well as magnitude for example velocity, displacement, position An arrow is placed above a symbol to indicate it is a vector (d, v ) Displacement/Position is a vector that describes the distance between 2 points and the change in direction that took place (d [E]) When writing the symbol for displacement always include the direction the object was moving in square brackets. The direction will always be given in the question. N = north, E = east and right = positive direction W = west, S = south and left = negative direction