SI Base Units unit of measurement Measurement, Significant Figures and Scien3fic Nota3on ► 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 ► Physical Science 2 SI Prefixes SI Derived Units ► Quan3ty Unit –  Area square meter
–  Volume
Cubic meter –  Density Kilograms per cubic meter
–  Pressure
pascal (kg/m ·∙ s2)
–  Energy joule (kg ·∙ m2/s2)
–  Frequency hertz (1/s) –  Electric Charge coulomb (A ·∙ s)
Symbol m2 m3 kg/m3 pa J Hz C 3 Uncertainty in Measurement 4 Exact Numbers ► There are 2 different types of numbers –  Exact 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 u  Infinitely important –  Measured u  measured with a measuring device u  these numbers will have a margin of ERROR 5 6 1
Learning Check Solu3on A. Exact numbers are obtained by 1. using a measuring tool 2. coun3ng 3. defini3on A. Exact numbers are obtained by 2. coun3ng 3. defini3on B. Measured numbers are obtained by 1. using a measuring tool B. Measured numbers are obtained by 1. using a measuring tool
2. coun3ng 3. defini3on 7 8 Uncertainty in Measurement ►  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 Uncertainty in Measurement ► A measurement always has some degree of uncertainty. Uncertainty in Measurement ► Different people es3mate differently. • 
Record all certain numbers and one estimated number.
2
What is the Length? Two measurements of the mass of the same
object. The same quantity is being described at
two different levels of precision or certainty.
1
2
3
4 cm
► We can see the markings between 1.6-­‐1.7cm ► 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 13 14 Learning Check Temperature Celsius to Fahrenheit •F= (9/5 x C) + 32 Fahrenheit to Celsius •C = 5/9(F-­‐32) Celsius to Kelvin •K = C+ 273 What is the length of the wooden s3ck? 1) 4.5 cm 2) 4.54 cm 3) 4.547 cm 16 Precision & Accuracy Rules for Coun3ng Significant Figures When reading a measured value, all nonzero digits are significant ► 
► 
1457
23.3
has 4 significant figures
has 3 significant figures
17 Chapter Two
18 3
Rules for Coun3ng Significant Figures of Zeros Prac3ce Rule 6 • All digits count Zeros 45.8736 a.  Leading zeros - never count
0.0025
2 significant figures
b.  Captive zeros - always count
1.008
4 significant figures
c.  Trailing zeros - count only if the number is
written with a decimal point
100
1 significant figure
100.
3 significant figures
120.0 4 significant figures
.000239 3 • Leading 0’s don’t .00023900 5 • Trailing 0’s do 48000. 5 • 0’s count in decimal form 48000 2 • 0’s don’t count w/o decimal 3.982×106 4 • All digits count 1.00040 6 • 0’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.
Chapter Two
22 Rounding Off Numbers ►  How do you decide how many digits to keep? ►  Simple rules exist to tell you how. 23 Chapter Two
24 4
►  RULE 1. If the first digit you remove is 4 or less, drop it and all following digits. Make the following into a 3 Sig Fig number u  2.4271 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  4.5832 is 4.6 when rounded off to 2 significant figures since the first dropped digit (an 8) is 5 or greater Chapter Two
1.56
.0037421
.00374
1367
1370
128,522
129,000
1.6683 ×106
1.67 ×106
Your Final number
must be of the same
value as the number
you started with,
129,000 and not 129
RULE 1. In carrying out a mul3plica3on or division, the answer cannot have more significant figures than either of the original numbers. For example you want a 4 Sig Fig number 4965.03 4965 0 is dropped, it is <5 780,582 780,600 8 is dropped, it is >5; Note you must include the 0’s 5 is dropped it is = 5; note you 2000. need a 4 Sig Fig 1999.5 1.5587
25 Examples of Rounding Prac3ce Rule #2 Rounding Chapter Two
Mul3plica3on and Division ► 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. Chapter Two
28 32.27 × 1.54 = 49.6958 49.7 3.68 ÷ .07925 = 46.4353312 46.4 1.750 × .0342000 = 0.05985 .05985 3.2650×106 × 4.858 = 1.586137 × 107 1.586 ×107 6.022×1023 × 1.661×10-­‐24 = 1.000000 1.000 29 5
Addi3on/Subtrac3on 25.5
+34.270 59.770
59.8
Addi3on and Subtrac3on 32.72
320 ‑ 0.0049 + 12.5 32.7151 332.5 32.72 330 .56 __ + . 153 ___ = . 713 __ .71 82000 + 5.32 = 82005.32 82000 10.0 -­‐ 9.8742 = .12580 .1 10 – 9.8742 = .12580 0 Look for the last important digit Mixed Order of Opera3on 8.52 + 4.1586 × 18.73 + 153.2 = = 8.52 + 77.89 + 153.2 = 239.61 = 239.6 Dimensional Analysis
(8.52 + 4.1586) × (18.73 + 153.2) = = 12.68 × 171.9 = 2179.692 = 2180. Conversion factor
§  A frac3on whose numerator and denominator are the same quan3ty expressed in different units §  Ex. 2.54 cm and 1 in. are the same length §  2.54 cm. = 1 in. §  Two conversion factors §  2.54 cm.
1 in. 1 in. 2.54 cm. Convert 8.50 in. to cm.
Desired unit
No. of cm. =
(8.50 in.)
2.54 cm.
= 21.6 cm
1 in.
Given unit
6
Note this!
Given unit
Desired unit
X
Given unit
=
Therefore:
Desired unit
Now let’s try this:
► 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?
Convert 185 lbs to grams
► A man weighs 185 lb. What is his mass in
grams?
–  Conversion factor = 1 lb = 453.6 g
► Determine the length in kilometers of a 500.0-mi
automobile race
–  Conversion factor = use your table of
conversion factors
Desired unit
No. of g. =
(185 lb.)
453.6 g.
= 83916 g
1 lb.
Given unit
Convert 500.0 miles to km
Resources Mackean, D. (2009). IGCSE Biology, 2nd ed. London, UK: Hodder Desired unit
No. of km=
500.0 miles
1.61 km
Educa3on. Mayhugh, J. (2015). Significant figures. Retrieved January 19, = 804.67 km
1 mile
Given unit
► Sig figs… 804.67km = 805km
► Remember, fewest amount of sf in problem are
reflected in answer
2015 from website www.lasalle.edu. 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