Exponential or scientific notation:

It is often convenient to express numbers in exponential or scientific notation to indicate significant figures, and to just avoid writing the huge numbers of zeros we often run into in the natural world. [covered in problem session]

SI Units (metric system)

SI Units: The metric system originated around the French Revolution as a rational system of measurements to rescue France from the chaos of pre-revolutionaary measurements and thus prevent tax collectors from cheating.

Wanted to base system on "natural" universal standards. Thus for length they chose the size of the Earth: specifically the meter was defined as one ten-millionth (10^-7) of the Earth's meridian (line from the S to the N pole) through Paris. For mass the Kilogram was defined as the mass of a cube of water 0.1 meter on a side. Of course these are not convenient, so standards were quickly created: the meter became the distance between two lines on a platinum-iridium bar stored in a vault in Paris, while the kilogram became a cylindrical mass of platinum-iridium stored in the same vault.

Today the various units are defined by international agreement to give the SI (Systéme International) units:

• Length: the meter (m) is defined as the distance light travels in a vacuum in 1/299,792,458 sec (note that this is truly universal: in principle it can be determined by anyone, anytime, anywhere in the Universe).
• Mass: the kilogram (kg) however is still based on the International Prototype Kilogram in Paris and the derived standard kilogram standards held by governments around the world.
• Time: the second (s) is defined today as the duration of 9,192,631,770 periods of the radiation of two hyperfine levels of the ground state of the cesium 133 atom.
• Amount of substance: the mole (mol) is defined as the number of atoms in 0.012 kg (defined, so sig figs not restricted) of carbon 12 atoms.
• Temperature: the kelvin (K) is defined as 1/273.15 of the thermodynamic temperature of the triple point of water.
• Electric current: the ampere is defined as the the current which carries one coulomb (6.24146 x 10¹⁸ times the charge on an electron or proton) of charge through a conductor in one second.

Prefixes: Note Table 1.2 in your text (p 9). You should know (memorize) and be able to interconvert the prefixes in the table below:

Prefix	Symbol	Magnitude
tera-	T	1012
giga-	G	109
mega-	M	106
kilo-	k	103
base		100
deci-	d	10-1
centi-	c	10-2
milli-	m	10-3
micro-	(or mc)	10-6
nano-	n	10-9
pico-	p	10-12
fempto-	f	10-15

Memorize: 1 mL = 1 cm³; 1 inch = 2.54 cm (defined); 1 liter is about 1 quart; density of water = 1 g/mL; 0° C = 32 °F, 100°C = 212 °F, -40 °C = -40 °F.

Temperature

Look in your text for conversions between °C and °F and example problems

Density

Density is defined as the mass of a given volume of a substance: Density = mass/volume. Note that this weeks laboratory exercise give practice in Density, significant figures etc.

Let's try some density problems. First note that the units of density are g/cm³ or g^.cm^-3.

• A student found that 20.0 mL of a liquid weighed 35.987 g. What is its density?

Known: Density = mass/volume, generally expressed as g/mL = g/cm³

Solve: (35.987 g) / (20.0 mL) = 1.79935 g/mL

note that the units are those of density so we are confident we set it up correctly.

How about sig figs? Use multiplication/division rules, so count: 3 for 20.0 and 5 for 35.987, therefore should have three sig figs:

1.79935 g/mL = 1.80 g/mL

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© R A Paselk

Last modified 26 January 2009