Allows us to work with very large or small numbers more easily. All numbers are a product of 10.

Transcription

1 Unit 1: Measurements Scientific Notation : Allows us to work with very large or small numbers more easily. All numbers are a product of 10. M x 10n M= signif. digit [ 1 < M < 10 ] n = an integer move the decimal point to make 1 non-zero digit, then count the number of places moved. if moved left... n is positive if moved right... n is negative. Math operations : Rules for Addition & Subtraction -- to add or subtract, these numbers need to be expressed with the same power of 10. Rules for Multiplying -- multiply the first factors [ M ] and add the exponents [ n ] Rules for Division -- divide the first factor in the numerator by the first factor in the denominator. Then subtract the exponent in denominator from the numerator.

2 Significant Figures In a measurement, they consist of all the digits known with certainty plus one final digit that is estimated. In any correctly reported value, the final digit is significant but not certain. Rules for significant digits digits other than zero are always significant or more final zeros - after the decimal point are always significant. 3. zeros between two other significant digits are always significant. 4. zeros used solely for spacing the decimal point are not significant. They are only placeholders. numbers are rounded off to make its degree of certainty match the original measurements. > 5 increase by < 5 stay the same nonzero increase odd # + 5 increase even # + 5 stay the same Rule for addition / subtraction : round the sum / difference so that it has the same number of decimal places as the measurement used having the fewest number of places. Rule for multiplication / division : express product / quotient obtained to the same number of digits as measurement having the fewer sig digs.

3 Accuracy vs. Precision are used to describe the reliability of a measurement Accuracy - how close a measurement is to the accepted or correct value for a quantity. Precision - how close a set of measurements for a quantity are to one another... reproducibility. see pg 44 for charts Percent Error a way to quantitatively compare accuracy to that of a correct or accepted value. Percent error is found by taking the absolute error, dividing it by the true value, and then multiplying it by 100%. ( Observed value ) - ( Accepted value ) = absolute error percent error = absoluteerror accepted error 100% Pg 45 # Pg 48 # and Pg 50 # 1 4 Pg 57 # 1-10

4 Units of Measure the result of nearly every measurement is a number and unit. measurements represent quantities, something that has a magnitude, size, or amount. It is not the same as a measurement. In 1960, scientists agreed on a single measurement system... Le Syste`me Internationale d Unites or SI. It has seven base units and other units derived from them. SI units are defined in terms of standard measurement, such as a objects or natural phenomena that are of constant value. prefixes are added to the names to represent larger or smaller base units...see pg 35

5 conversion factors are ratios used to convert a unit to any other related unit. We need to create an equivalence statement between units [the bridge], which can cancel each other out...each factor equals 1. Factor label method is a system for doing conversions, where unit labels are treated as factors. Pg 42 # 1 6

6 Derived SI Units: these are combinations of quantities and are produced by multiplying / dividing standard units...see pg 36. Volume - the amount of space occupied by an object; where the standard is in cubic meters (m3). o 1 m3 = cm3 o 1 dm3 = 1000 cm3 = 1 liter o 1 cm3 = 1 ml Density - the ratio of mass to volume. o density = mass / volume or D = m / v SI unit is kg / m3 Density is a physical property, it does not depend on sample size b/c volume increases proportionately. Density varies w/ temperature; most objects expand as temperature increases, causing an increased volume --> the density drops. Pg 54 # 1-4

7 Graphing : Direct proportions - two quantities are directly proportional, if dividing one by the other gives a constant value. this produces a straight line. y / x = k or Y = k x y x Inverse proportions - two quantities are inversely proportional if their product is constant. if x increases, y must decrease to keep product constant this produces a hyperbola. y 1/x or x y = k y x Pg 57 # 1-9

8 Graphing Techniques When plotting a graph, take the following steps. 1. Identify the independent and dependent variables. 2. Choose your scale carefully. Make your graph as large as possible by spreading out the data on each axis. Let each space stand for a convenient amount. To avoid a cluttered appearance, you do not need to number every space. 3. All graphs do not go through the origin (0,0). Think about your experiment and decide if the data would logically include a (0,0) point. 4. Plot the independent variable on the horizontal [x] axis and the dependent variable on the vertical [y] axis. Plot each data point. 5. Label each axis with the name of the variable and the unit. Using a ruler, darken the lines representing each axis. 6. If the data points appear to lie roughly in a straight line, draw the best straight line you can with a ruler and a sharp pencil. Have the line go through as many points as possible with approximately the same number of points above the line as below. NEVER connect the dots. If the points do not form a straight line, draw the best smooth curve possible. 7. Title your graph. The title should clearly state the purpose of the graph and include the independent and dependent variables.

9 Mass [g] Volume [ml] Plot a graph and draw the best curve to fit your data at the left