SI Base Units unit of measurement. Measurement, Significant Figures and Scien3fic Nota3on. SI Prefixes. SI Derived Units. Uncertainty in Measurement

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1 Measurement, Significant Figures and Scien3fic Nota3on Physical Science SI Base Units unit of measurement ampere (A) - electric current kilogram (kg) - mass metre (m) - length second (s) - 3me kelvin (K) - thermodynamic temperature mole (mol) - amount of substance candela (cd) - luminous intensity 2 SI Derived Units SI Prefixes Quan3ty Unit Symbol Area square meter m 2 Volume Cubic meter m 3 Density Kilograms per cubic meter kg/m 3 Pressure pascal (kg/m s 2 ) pa Energy joule (kg m 2 /s 2 ) J Frequency hertz (1/s) Hz Electric Charge coulomb (A s) C 3 4 There are 2 different types of numbers Exact u Infinitely important Measured u measured with a measuring device u these numbers will have a margin of ERROR Exact Numbers An exact number is obtained when you count objects or use a defined rela3onship. Coun3ng objects are always exact 2 soccer balls 4 pizzas Exact rela3onships, predefined values, not measured 1 foot = 12 inches 1 meter = 100 cm 1 inch = 2.54 cm 5 6 1

2 Learning Check A. Exact numbers are obtained by 1. using a measuring tool 2. coun3ng 3. defini3on B. Measured numbers are obtained by 1. using a measuring tool 2. coun3ng 3. defini3on Solu3on A. Exact numbers are obtained by 2. coun3ng 3. defini3on B. Measured numbers are obtained by 1. using a measuring tool 7 8 Every experimental measurement has a degree of uncertainty. The volume, V, at right is certain in the 10 s place, 10mL<V<20mL The 1 s digit is also certain, 17mL<V<18mL A best guess is needed for the tenths place. A man with a watch knows what 3me it is. A man with two watches is never sure (Unknown) 9 A measurement always has some degree of uncertainty. Different people es3mate differently. Record all certain numbers and one estimated number. 2

3 Two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty. What is the Length? cm We can see the markings between cm We can t see the markings between the.6-.7 We must guess between.6 &.7 We record 1.67 cm as our measurement The last digit an 7 was our guess...stop there Learning Check Temperature Celsius to Fahrenheit F= (9/5 x C) + 32 Fahrenheit to Celsius C = 5/9(F- 32) What is the length of the wooden s3ck? 1) 4.5 cm 2) 4.54 cm 3) cm Celsius to Kelvin K = C Precision & Accuracy Rules for Coun3ng Significant Figures When reading a measured value, all nonzero digits are significant 1457 has 4 significant figures 23.3 has 3 significant figures

4 Rules for Coun3ng Significant Figures of Zeros Prac3ce Rule 6 All digits count Zeros a. Leading zeros - never count significant figures b. Captive zeros - always count significant figures c. Trailing zeros - count only if the number is written with a decimal point significant figure significant figures significant figures Leading 0 s don t Trailing 0 s do s count in decimal form s don t count w/o decimal All digits count s between digits count as well as trailing in decimal form Scien3fic Nota3on Scien3fic Nota3on a convenient way to write a very small or a very large number Numbers are wrilen as a product of a number between 1 and 10, 3mes the number 10 raised to power. 21 Two examples of converting scientific notation back to standard notation are shown below. 22 Rounding Off Numbers How do you decide how many digits to keep? Simple rules exist to tell you how

5 RULE 1. If the first digit you remove is 4 or less, drop it and all following digits. u becomes 2.4 when rounded off to two significant figures RULE 2. If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept. u is 4.6 when rounded off to 2 significant figures since the first dropped digit (an 8) is 5 or greater Prac3ce Rule #2 Rounding Make the following into a 3 Sig Fig number , , Your Final number must be of the same value as the number you started with, 129,000 and not Examples of Rounding For example you want a 4 Sig Fig number RULE 1. In carrying out a mul3plica3on or division, the answer cannot have more significant figures than either of the original numbers is dropped, it is <5 780, , is dropped, it is >5; Note you must include the 0 s 5 is dropped it is = 5; note you need a 4 Sig Fig 28 RULE 2. In carrying out an addi3on or subtrac3on, the answer cannot have more digits aoer the decimal point than either of the original numbers. Mul3plica3on and Division = = = = =

6 Addi3on/Subtrac3on Addi3on and Subtrac3on = = = Look for the last important digit = Mixed Order of Opera3on = = = = Dimensional Analysis ( ) ( ) = = = = Conversion factor Convert 8.50 in. to cm. A frac3on whose numerator and denominator are the same quan3ty expressed in different units Ex cm and 1 in. are the same length 2.54 cm. = 1 in. Two conversion factors 2.54 cm. 1 in. 1 in cm. No. of cm. = 2.54 cm. (8.50 in.) 1 in. = 21.6 cm 6

7 Note this! Therefore: X = What data are you given in the problem? What quantity do you wish to obtain in the problem? What conversion factors do you have available to take you from the given quantity to the desired one? Now let s try this: Convert 185 lbs to grams A man weighs 185 lb. What is his mass in grams? Conversion factor = 1 lb = g Determine the length in kilometers of a mi automobile race Conversion factor = use your table of conversion factors No. of g. = (185 lb.) g. 1 lb. = g Convert miles to km Resources No. of km= miles 1.61 km 1 mile = km Sig figs km = 805km Remember, fewest amount of sf in problem are reflected in answer Mackean, D. (2009). IGCSE Biology, 2 nd ed. London, UK: Hodder Educa3on. Mayhugh, J. (2015). Significant figures. Retrieved January 19, 2015 from website Miller, K., Levine, J. (2012). Biology. Pearson Educa3on, Inc. Boston. Postlethwait, J. and Hopson, J.(2006). Modern Biology. Aus3n, TX. Holt, Reinhart, Winston. 42 7