Units of Measurement Base Units Derived Units Length meter (m) Volume SI units (Systeme Internationale d’Unites) were developed so that scientists could duplicate and communicate their work. A unit that is defined by a combination of a base units. Base Units Derived Units Length meter (m) Volume meter cubed (m3) Mass kilogram (kg) Density grams per cubic centimeter (g/cm3) Time second (s) Temperature kelvin (K)

Units of Measurement

Metric Conversions Move the decimal to the right Move the decimal to the left Every metric unit is different from its neighbor by a factor of ten When converting between two units the decimal point is moved the number of places equal to the distance between the two unit in the chart above and in the same direction of movement

Sample problem Convert the following Start with 53. Move the decimal to the right Move the decimal to the left Convert the following 53 hg = ________dg Start with 53. Move the decimal 3 spaces to the right 53 Fill in the empty spaces with zeros 53000 dg

Sample Problem Start with 300. Move the decimal to the right Move the decimal to the left Convert the following 300 cg = ________kg Start with 300. Move the decimal 5 spaces to the left 300 Fill in the empty spaces with zeros 0.00300 kg

More Practice Problems Convert the following 0.058 dam = _______ dm 0.25 cL = _______ L 109 hg = ________ mg 5.8 0.0025 10900000

Units of Measurement Derived Units… A unit that is defined by a combination of base units is called a derived unit. Volume: the space occupied by an object. The metric unit for volume equal to one cubic decimeter (dm3) is a liter (L). Density: a ratio that compares the mass of an object to its volume. The units for density are often grams per cubic centimeter (g/cm3). Formula –

Density Ratio of an object’s mass to its volume What happens to density when mass is constant and volume changes?

Mass, Volume and Density Relationships DIRECT INDIRECT

Density Problem Example… Suppose a sample of aluminum is placed in a 25-ml graduated cylinder containing 10.5 ml of water. The level of the water rises to 13.5 ml. What is the mass of the aluminum sample if its density is 2.70 g/ml? FORMULA _______________ NEW FORMULA _______________ PLUG-IN NUMERICAL VALUES (with units) SOLVE (answer)

Temperature Scales Temperature… The temperature of an object is a measure of how hot or cold the object is relative to other objects.

Homework #1 Page(s) 30 Problem(s): 4, 5, 6, 10, and 11

What is the significance of this number? Pre-Class Activity 602000000000000000000000 What is the significance of this number? How would you express this number in scientific notation?

Scientific Notation 6.02 x 1023 Exponent Coefficient The coefficient must be greater than or equal to one and less than 10. When expressing numbers less than one (ex. 0.001) in scientific notation, the decimal point is moved to the right until the coefficient is within range. The number of spaces moved is used to determine the exponent. For numbers less than one, the exponent is negative When expressing numbers greater than 10 (ex. 1000) in scientific notation, the decimal point is moved to the left until the coefficient is within range. The number of spaces moved is used to determine the exponent. For numbers greater than 1, the exponent is positive.

Scientific Notation Calculations Multiplication and Division For multiplication, multiply the coefficients and add the exponents (1.3 x 104) x (2.0 x 106) = Remember, your final answer must be in the correct form. Often, multiplication of coefficients will yield a number greater than 10. In this case the result must be changed into the proper form. (5.3 x 104) x (2.0 x 106) = = For division, divide the coefficients and subtract the exponents. Often, division of coefficients will result in a value that is less than one. If this occurs, the final result must be changed into the proper form. (2.0 x 10-3)  (4.00 x 104) = = 2.6 x 1010 10.6 x 1010 1.06 x 1011 0.5 x 10-7 5 x 10-8

Scientific Notation Calculations Addition and Subtraction In order to add or subtract numbers in scientific notation, the exponents of each number has to be the same As a rule of thumb, it is best to take the number with the lower exponent and change it match the higher exponent. To increase an exponent, move the decimal point in the coefficient to left, the number of spaces equal to the increase in the exponent. Once the exponents are equal, the coefficients can be added or subtracted 2.1 x 104 + 1 x 103 2.1 x 104 + 0.1 x 104 2.2 x 104 5.37 x 10-4 - 6.2 x 10-5 5.37 x 10-4 0.62 x 10-4 4.75 x 10-4

Homework #2 Page(s) 32-33 Problem(s): 13, 14(a-d), 15(a, b), 16(a, b)

Factor Label Method of Conversion 100 cm = 1 m 1 m = 100 cm Use conversion factors to systematically move from one unit to the next, cancelling out units on the diagonal in each step. Convert 18 m = _______ cm 100 cm 18m = 1800 cm 1 m

Multistep Factor Label Problems Convert 350 tsp = ______ L Using the following conversion factors 1 tsp = 5 mL 1 L = 1000 mL 5 mL 1 tsp 1 L 1000 mL 350 tsp = 1.75 L

Multistep Factor Label Practice Convert 3 min= ______ms Use 1 min=60 s and 1000 ms = 1 s Convert 32oz = _____ g Use 16 oz=1 lb, 2.2 lb = 1kg, 1kg=1000 g

Multidimensional Factor Label Problems Convert 25 g/mL = ______ kg/dL Convert one unit at a time Recognize that one unit is in the denominator 25 g 1 mL 1 Kg 100mL 1 dL =2.5kg/dL 1000 g

Multidimensional Factor Label Practice Convert 85 km/hr = _________m/s Convert 0.6 L/min = ________ qt/hr Use 1qt = 1.1L

1 ft = 12in Factor Label Practice for Area and Volume Remember to square or cube the unit as well as the number when converting to a squared or cubed unit 1 ft = 12in    

Homework #3 Page(s) 34-35 Problem(s): 17 and 21

Pre-class Activity How long is this paperclip? To what degree of certainty can it be measured?

Significant Figures in Measurement Scientists determine the precision of instruments by the number of digits they report.

Significant Figures in Measurement Measurements always include all certain digits and one uncertain digit. 52.7 mL

Measurement Challenge What value would you assign to each of these measurements? _________ mL _________ cm

Identifying Significant Figures in Numbers When examining a number, you determine the number of digits that are significant by the following rules: All non-zero numbers are significant All final zeros to the right of a decimal are significant Zeros between significant digits are significant For positive numbers less than one, all zeros directly after the decimal before the first significant figure are not significant. All zeros at the end of a whole number are not significant. All contants and counting numbers have an unlimited number of significant figures. 4. 5.

Sig Fig Challenge How many sig figs are there in the following numbers: 0.0004 687 1.0082 330 70.2080

Sig Fig Rules for Calculations Multiplication and Division Your answer can not contain more or less sig figs than the operator that contains the least number of sig figs. 3.86 x 0.45=1.737 1.7 1.737 Identify the significant figures, look on place beyond. If that digit is 5 or above, round up. If it is less than 5 drop off.

Sig Fig Rules for Calculations Addition and Subtraction Your answer can not be more precise than the least precise operator. Most of the time this means that your answer must have the same number of decimal places as the least precise operator 12.38 cm +2.5 cm 14.88 cm 14.9 cm 1060 cm + 23.5 cm 1083.5 cm 1080 cm If one of the numbers is a whole number that ends in zero(s), then the final answer must be rounded to the lowest place that contains a nonzero number.

Reliability of Measurements Accuracy vs. Precision How close a measured value is to an accepted value How close a series of measurements are to one another High Accuracy High Precision Low Accuracy High Precision Low Accuracy High Accuracy

Percent Error Used to evaluate the accuracy of experimental data.

Homework #4 Page(s) 38-42 Problem(s): 29, 31, 33, 35, 37(a, b), 38(a, b)

Representing Data Graphing Circle Graphs (based on percents) Bar Graphs (How quantities vary)

Graphing continued Line Graphs In science, we draw a best fit line between data points. Do not connect the dots. Dependent Variable Dependent Variable Independent Variable Independent Variable Which graph shows and indirect relationship between the dependent and independent variable?

Calculating the Slope of a Best Fit Line Select two points on the line that you have drawn. Do not select two of your data points because they might not fall on the line.

Line Graph Basics Graphing Reminders… Fit the page Graph title Consistent x-axis and y-axis scales Labeled (with units) x-axis and y-axis Best fit line DO NOT CONNECT THE DOTS!

Review Assignment Page 50 Problem(s): 52, 57, 59, 73, 75 (a, b, c, and d), and 76 (a, b, c, and d) Page 51 Problem(s): 77 (b, d, e, g, h, and i), 78 (a, e, and f), 80 (a, b, c, d, e, and f), 82 (a and c), 84 (c, e, and f), 85 (a, b, c, and d), and 86 (a, b, c, and d) Page 52 Problem(s): 87 Page 53 Problem(s): 1, 3, 5, 7, and 9