Numbers in Science Chemists deal with very large numbers… (Do you recognize this number?)

Count the Zeros… m/s That isn’t much fun! There must be a better way!?! 5 ZEROS 24 ZEROS

Scientific Notation  There is a way!!! HURRAY!!!  S.N. is a way of making these numbers easier to write.

To write these numbers in scientific notation, move the decimal so that it is expressed as:  A number between 1 and 10  Times ten to a power

Practice problems  12300=  2.5 X 10 3 =  1.0 X =  2.05 X =

The Importance of Units  Numbers are used in science for quantifying measurements.  However, all numbers must be followed by a unit!!  Naked numbers have no meaning in science! Thus will never receive full credit!

Measurements in Science  Observations in science should be quantified whenever possible.  For this reason, scientists (you) must master the tools used for measuring and the units that are used to express them.

General rules for measurement  All units will be metric. Memorize the units for: Length = meter (m) Length = meter (m) mass = gram (g) mass = gram (g) volume = liter (L) volume = liter (L)

Prefixes used with the basic units  Kilo or 10 3  Centi- 1/100 th or  Milli- 1/1000 th or 10 -3

Practice 1 kg = g1 m = cm 1 km = m1 L = mL 1 cm = m1 cm = mm 1 mL = L

Significant Figures (Digits)  Pay attention to the precision of your tools  Record all of the numbers in a measurement that you are certain of, plus one more (an approximation) called “the uncertainty.”  All of the measured numbers, plus the uncertain number are called significant figures.

Why are they important? 1.They communicate the precision of the measuring tools used by the chemist. 2.They determine how precise the answers to calculations (using the measuring tools) can be.

Example…

Another Example… 94 mL 95.0 mL

Significant Figure Rules: 1.All non zero numbers are always significant. 2.Zeros between non-zero numbers are always significant. 3.Leading zeros are never significant. 4.Trailing zeros are not significant if the number has no decimal point. 5.Trailing zeros are significant if the number has a decimal point. 6.The mantissa (number in front of the power of ten) of a number written in scientific notation is always significant. The power of ten is not.

Practice! Determine how many significant figures each has identify which rules tell you this cm = 35.0 s = kg = m = 2.5 x mL =

Sig. Figs in Calculations Multiplying or dividing – the number of significant figures in the answer must be the same as the number of significant figures for the least accurate measurement used in the problem. Ex: What is the density of an object with a mass of g and a volume of 3.3 mL? Calculator says  g/mL Correct sig figs  3.0 g/mL

What about (+) and (-)? Adding or subtracting – the number of decimal places in the answer must be the same as the smallest number of decimal places in the measurements used to make the calculation. Ex: mm mm mm = Calculator says  mm Correct sig figs  21.1 mm

Do you and your calculator have a communication problem?  Solve the problem below using your calculator. 3.0 x 10 5 = 1.5 x 10 2 * 2.0 x 10 3