Measurements Number followed by a Unit from a measuring device SI Units (Le Système international d'unités) – based on the metric system Time second (s) Length meter (m) Mass kilogram (kg) Temperature Kelvin (K) Amount of a substance mole (mol)

Metric Prefixes

What is Scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise. For very large and very small numbers, scientific notation is more concise.

Scientific notation consists of two parts: A number between 1 and 10 A power of 10 N x 1 0 x

Conversion factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Dimensional Analysis (Factor-label method) A way of solving problems using conversion factors By using dimensional analysis the UNITS ensure that you have the conversion factor in the proper arrangement

Significant Figures The numbers reported in a measurement are limited by the measuring tool Significant figures in a measurement include all; the known digits plus one estimated digit

Which of the two clocks below has the potential to be the most accurate? Why?

Comparing Rulers

Zero as a Measured Number Last (estimated) digit is 5.00 cm . l3. . . . I . . . . I4 . . . . I . . . . I5. . cm What is the length of the line? First digit 5.?? cm Second digit 5.0? cm Last (estimated) digit is 5.00 cm

Reading a Meterstick . l2. . . . I . . . . I3 . . . .I . . . . I4. . cm First digit (known) = 2 2.?? cm Second digit (known) = 0.7 2.7? cm Third digit (estimated) between 0.05- 0.07 Length reported = 2.75 cm or 2.74 cm or 2.76 cm

Rules for Significant Figures adapted from Russo's Reliable Rules for Significant Figures All non-zero digits are significant Zeroes between non-zero digits are significant In measurements containing an expressed decimal, zeros to the right of NON-ZERO digits are significant.

“Atlantic - Pacific Rule” Count from the ocean towards the coast starting with the first nonzero digit, and include all the digits that follow.

Significant Numbers in Calculations A calculated answer cannot be more precise than the measuring tool. A calculated answer must match the least precise measurement. Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing

Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places. Practice: 2.45 cm + 6.382 cm + 5.8 cm 18.92 mL - 10.42 mL 22.100 g -13 g + 2.93g 14.6 cm 8.50 mL 12 g

Multiplying and Dividing Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures. Practice: 4.20 m x 3.21 m x 0.16 m 100.35 g / 90.2 mL (3.28 x 10-5 km) / (4 x 102 s) 2.2 m3 1.11 g/mL 8 x 10-8 km/s

Temperature Scales Fahrenheit Celsius Kelvin Anders Celsius 1701-1744 Lord Kelvin (William Thomson) 1824-1907

Temperature Scales Kelvin Celsius 373 K 100 ˚C 100 K 100˚C 273 K 0 ˚C Boiling point of water 373 K 273 K 100 K 100 ˚C 0 ˚C 100˚C Freezing point of water Notice that 1 kelvin = 1 degree Celsius

K = ˚C + 273 Calculations Using Temperature Generally require temp’s in Kelvin K = ˚C + 273 Body temp = 37 ˚C + 273 = 310 K Liquid nitrogen = -196 ˚C + 273 = 77 K

Derived Units – a combination of 2 or more base units Area (length x length) Speed (length per time) Volume (length x length x length) Density (mass per volume)

DENSITY Aluminum Platinum Mercury 13.6 g/cm3 21.5 g/cm3 2.7 g/cm3

Volume Displacement 25 mL A solid displaces a matching volume of water when the solid is placed in water. 33 mL 25 mL

Learning Check What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/ cm3 2) 6 g/cm3 3) 252 g/cm3

Solution Volume (mL) of water displaced = 33 mL - 25 mL = 8 mL Volume of metal (cm3) = 8 mL x 1 cm3 = 8 cm3 1 mL Density of metal = mass = 48 g = 6 g/cm3 volume 8 cm3

Can you hit the bull's-eye? Three targets with three arrows each to shoot. How do they compare? Both accurate and precise Precise but not accurate Neither accurate nor precise Can you define accuracy and precision?

How can someone show the accurate the measurement? Calculation of percent error (Value accepted - Value experimental) Value accepted Percent Error (%) = x 100

Graphing Data Bar graphs Circle graphs Line graphs Directly proportional Inverse proportional