Chemistry Mathematics

Measurement3221.MATH.1; 3221.MATH.2

Learning Goals• Write the names and abbreviations for the

units used in measurements of length, volume, and mass

• Label measurements as accurate or precise• Write a number in scientific notation• Determine the number of significant figures

in measured numbers• Adjust calculated answers to the correct

number of significant figures.• Use numerical prefixes to do metric

conversions through decimal placement.

Units of Measurement• 2 parts to any measurement: number and unit• Units are extremely important in reporting

and working with scientific numbers and they must be included

• The number of digits in a measurement reflects a degree of precision: the more digits in the measurement, the more precise it is; fewer digits, less precision

Why is this important??

Read the following:

• When my son was 7 he walked 3, and when he was 4 he threw his baseball 8 and said his school was 5 away.

• When my son was 7 months old he walked 3 steps, and when he was 4 years old he threw his ball 8 feet and said his school was 5 minutes away.

• The units make all the difference!!!

Uncertainty in Measurement

• Accuracy: how close a measurement is to the accepted value

• Precision: degree of “agreement” between several measurements of the same quantity

• A MEASUREMENT CAN ONLY BE AS PRECISE AS THE INSTRUMENT USED!!!

Accuracy and Precision Illustration

Two major systems:

1. English system-used only in the United States-inches, yards, pounds

2. Metric system-International System (SI system) is the system of

measurement for the scientific world-centimeters, meters, kilograms

Fundamental SI Units

Quantity Symbol Unit name Unit abbreviation

Length l Meter m

Mass m Kilogram kg

Time t Second s

Temperature T Kelvin K

Amount of substance n Mole mol

Electric current I Ampere A

Luminous intensity Iv Candela cd

What do the units mean?• Unit: predefined standard of measurement or

basis of comparison• Second: 60 s = 1 min• 1 meter is slightly longer than 1 yard a 100

yd football field is only 91.4 m• 1 kg = 2.205 lb

Remember: mass is different than weight, which is affected by gravity

Prefixes in SI systemPrefix Symbol Meaning Exponential Notation

mega- M 1,000,000 106

kilo- k 1,000 103

hecto- h 100 102

deka- da 10 101

------ ----- 1 100

deci- d 0.1 10-1

centi- c 0.01 10-2

milli- m 0.001 10-3

micro- µ 0.000001 10-6

nano- n 0.000000001 10-9

Prefix Multipliers• Used with the standard units of the SI system,

rather than having different “units” with which to make comparisons

• Multipliers change the value of the unit by powers of 10

• Prefix multipliers allow us to express a wide range of measurements in units that are similar in size to the quantity we are measuring– Choose the prefix that is most convenient for a

particular measurement

Derived SI UnitsQuantity Symbol Unit name Abbreviation Derivation

Area A Square meter m2 Length x width

Volume V Cubic meter m3 Length x width x height

Density D kg/ m3 Mass/volume

Molar mass M kg/ mol Mass/amt of substance

Molar volume Vm m3/ mol Volume/ amt of substance

Energy E Joule J Force x length

ANY UNIT OF LENGTH, WHEN CUBED (RAISED TO THE THIRD POWER), BECOMES A UNIT OF VOLUME

1 cm3 = 1 mL 1 dm3 = 1 L

Uncertainty in Measurements• Measured numbers: numbers you obtain when

you use a measuring tool to determine your height, weight, or temperature

• To report a measurement, first read the numerical value of the marked line. Finally, estimate between the smallest marked lines.

• When an estimate ends on a marked line, a zero is written for the estimated digit.

Significant Figures

Scientific numbers are recorded so that every digit is certain except for last, which is estimated.

48.872

When recording measurements, only estimate ONE digit beyond the smallest division on the instrument being used!!

Reading Volume• Meniscus: the curved portion at

the top of a volume of liquid• Most liquids have a concave

meniscus, however mercury has a convex meniscus

Rules for determining significant figures:1. All nonzero digits are significant

1.05 0.01102. Interior zeros (zeros between 2 numbers) are significant

1.0208 50.13. Trailing zeros (zeros after a decimal point) are significant

5.10 3.004. Leading zeros ( zeros to the left of the first nonzero number) are not significant. They only serve to locate the decimal point.

0.00005

Practice Problems

1. 0.007892. 2.00123. 0.0014. 4.1005. 0.10006. 2.650017. 100.25

Solutions to Problems

1. 0.00789 3 significant figures (0.00789)2. 2.0012 5 (2.0012)3. 0.001 1 (0.001)4. 4.100 4 (4.100)5. 0.1000 4 (0.1000)6. 2.65001 6 (2.65001)7. 100.25 5 (100.25)

Exact numbersExact numbers have an unlimited number of significant figures• 3 sources

1. accurate counting of discrete objects3 atoms means 3.000000 atoms

2. defined quantities100 cm = 1 m means 100.000 cm =1.00m

3. integral numbers that are part of an equation

radius = diameter/ 2

Significant Figures in Calculations

• In multiplication or division, the result carries the same number of significant figures as the factor with the fewest significant figures

• In addition or subtraction, the result carries the same number of decimal places as the quantity carrying the fewest decimal places

Scientific Notation• Used to write cumbersome numbers in a compact

manner1.2 x 10-10 exponent (n)

Decimal part exponential part

To convert a number to scientific notation:1. move the decimal point to obtain a number between 1 and

10.2. multiply by 10 raised to the number of places you moved the

decimal point-if decimal moved left: positive exponent-if decimal moved right: negative exponent

Practice

Percent Error• The percentage by which a

measurement deviates from the accepted value

• NO MEASURED VALUE WILL EVER BE EXACT!!

• % Error = Accepted Answer - Experimental Answer x 100

Accepted Answer

Practice Problems1. Samantha S. Sloppiness measured the volume of her soda before she drank it

for her midmorning snack. She measured the volume of the 12 oz. bottle to be 14 oz.

2. Clyde Clumsy was directed to weigh a 500 g mass on the balance. After diligently goofing off for ten minutes, he quickly weighed the object and reported 458 g.

3. Pretty Patty Pestilence had casually recorded her grades for the nine weeks in her notebook. She concluded she had 250 points out of 300 for the grading period. However, Miraculous (chemistry teacher) determined she had 225 points out of 300 and awarded her a "C" for the grading period.

4. Drew D. Ditzy came to Miraculous with a problem. Drew was told to measure 50 cm of copper wire to use in an experiment. Since his ruler only measured to 45 cm he used this amount of wire and his experiment was a failure.

5. Henry Heavyfoot was just arrested for speeding by Officer O'Rourke for traveling 65 mph in a 55 mph zone. Henry claimed his speedometer said 55 mph not 65 mph.