1. Measuring and Calculating Chapter 2

2. n Scientific method- a logical approach to solving problems n -Observation often involves making measurements and collecting data. The data may be –Qualitative- descriptive (non-numerical) –Quantititative- numerical –What are some examples of each type?

3. Measurement n Measurements represent quantities. –A quantity is something that has magnitude, size, or amount. A quantity is NOT the same as a measurement. –Units of measurement compare what is to be measured with a previously defined size. Ex. A teaspoon of volume. The teaspoon is the measurement and volume is the quantity.

4. Significant Figures n Indicate precision of a measurement. n Recording Sig Figs –Sig figs in a measurement include the known digits plus a final estimated digit

5. Significant Figures  Count all numbers EXCEPT:  Leading zeros -- 0.0025  Trailing zeros without a decimal point -- 2,500  ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant.  ALL zeroes between non-zero numbers are ALWAYS significant.

6. Significant Figures n Any zero to the right of a non-zero digit is significant if there is a decimal in the number. –Example: 0.070 ml

7. Significant Figures

8. n Calculating with Sig Figs –Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. n (13.91g/cm 3 )(23.3cm 3 )= 324.103g 4 sf 3 sf 324g

9. Significant Figures n Calculating with Sig Figs (con’t) –Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

10. Scientific Notation n Large Numbers 35,000,000 = 3.5x10 7 n Small Numbers 0.00061 = 6.1 x 10 -4

11. Scientific Notation 65,000 kg  6.5 × 10 4 kg n Converting into Sci. Notation: –Move decimal until there’s 1 digit to its left. Places moved = exponent. _____. _____ _____ × 10 x –Large # (>1)  positive exponent Small # (<1)  negative exponent –Only include sig figs.

12. Mathematical Operations using Scientific Notation n Multiplication –Numbers are multiplied and exponents are added algebraically. n Division –Numbers are divided and the exponent of the denominator is subtracted from that of the numerator.

13. Scientific Notation n Calculating with Sci. Notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = Type on your calculator: n = 671.6049383 = 670 g/mol = 6.7 × 10 2 g/mol

14. Scientific Notation n (3 x 10 3 ) x (4 x 10 -5 )= n (4 x 10 -6 ) / (2 x 10 3 )=

15. SI Measurement n Le Systeme International d’Unites n Adopted in 1960. n Has 7 base units. –Most other units are derived from these base units.

16. SI Base Units n Mass (kg) n Length (m) n Time (s) n Temperature (kelvin) n Amount of substance (mol) n Electric current (ampere) n Luminous intensity (candela)

17. Mass n Recall that mass is a measure of the quantity of matter. n Not the same as weight. –Weight is a measure of the gravitational pull on matter.

18. Length n SI standard unit is the meter (m). –Average width of a doorway is 1 m. –See table 2.1 on page 38 for more on standard units of measurement.

19. Metric Prefixes n Nano: n - 10 -9 – one billionth Micro:  -  10 -6 – one millionth n Milli: m - 10 -3 – one thousandth n Centi: c - 10 -2 – one hundredth n Deci: d – 10 -1 – one tenth n Kilo: k - 10 3 – one thousand n Mega: M - 10 6 – one million n See table 2.2 on page 39 for more.

20. Derived SI Units n Area=length x width n Volume –When measuring the volume of liquids and gases use a non-SI unit called the liter. 1 L = 1000cm 3 = 1000mL 1 ml = 1 cm 3

21. Density Table on pg 38. n Density is the ratio of mass to volume or mass divided by volume. –Density = mass / volume (D=m/v) n Expressed as g/mL or g/cm 3 n Intensive physical property of a substance—it does not depend on the size of the sample. –Why? n Affected by temperature.

22. Practice Problems n A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm 3. Calculate the density of aluminum. n What is the volume of a sample of liquid mercury that has a mass of 76.2 g, given the density of mercury is 13.6 g/mL?

23. Conversion Factors n A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other. n Conversion factors are always equal to one.

24. Examples of conversion factors n 1 meter = 100 centimeters n 1000 meters = 1 kilometer n 10 decimeters = 1 meter n 1 meter = 1000 millimeters n Can you think of any others?

25. Dimensional Analysis n Use conversion factors to solve problems. n Way of manipulating conversion factors to get answers in desired units. n See “Intro to Dimensional Analysis Problems” handout.

26. Practice: n Complete the following conversions: 1. 10.5 g = ___ kg 2. 1.57 km = ___ m 3. 3.54  g = ___ g 4. 3.5 mol = ___  mol

27. Proportions n Direct Proportion  Inverse Proportion y x y x

28. Accuracy and Precision n Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. –Measured values that are accurate are close to the accepted value. n Precision refers to the closeness of a set of measurements of the same quantity made in the same way. –Measured values that are precise are close to one another but not necessarily close to the accepted value.

29. n Look at each picture. Are the darts accurate, precise, or both?

30. Percent Error n The accuracy of an individual value or of an average experimental value can be compared quantitatively with the correct or accepted value by calculating the percent error. n % error = (Value experimental -Value accepted ) x 100 Value accepted

31. Practice Problems n A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.36 g/mL. What is the % error of the student’s measurement? n What is the % error for a mass measurement of 17.7 g, given that the correct value is 21.2 g?