Measurement and Calculations

Scientific Notation• Is used to represent very small and very large

numbers easily so that they are easy to write and read with less errors

• Large numbers are represented by a positive exponent of ten• 9.8 x 1012 = 9,800,000,000,000

• Small numbers are represented by a negative exponent of ten• 9.8 x 10-12 = 0.0000000000098

• See textbook review/rules list p. 127

Measurements• A measurement always consists of two parts: a

number and a unit• The unit tells the reader what scale/standard was

used and makes the number meaningful• Scientists use the SI (System Internationale in

French) system of units based upon the metric system

Measurement

Unit Instrument

Length Meter Meter stick

Mass Gram Balance

Volume Liter Graduated cylinder

Uncertainty in Measurements• Every measurement has some degree of

uncertainty• This is dependent upon the instrument used for

measuring

• All numbers recorded in a measurement = the significant figures of that measurement• They include all certain numbers plus the first uncertain

number• Ex: if the uncertainty for a measurement of 1.86 is

+/- .01, then the measurement could actually be: 1.86, 1.85, or 1.87

Rules for Determining # of Sig Figs

1. All nonzero numbers are significant2. Zeros are sometimes significant

a) Leading zeros are never significant (.0025 has only 2 sig figs)

b) Captive zeros are always significant (.2005 has 4 sig figs)

c) Trailing zeros are sometimes significant Only if there is a decimal point in the number No decimal point means those zeros are not significant Ex: 20 has one sig fig, 20. has two sig figs , 20.0 has

three sig figs The number of sig figs in the examples above alert the

reader as to the type of measurement device used

Rounding Off• Your final answer can never have more sig figs

than the least precise measurement.• Rounding off your answer can accomplish this• If the number to be removed is less than five, the

preceding digit remains the same• If the number to be removed is/is greater than five, the

preceding digit is increased by one• If you are doing a series of calculations, round at the last

step only, not at each separate intermediary step

How to Determine the Number of Sig Figs in a Calculation for Rounding Purposes

• For multiplication and division, your answer should contain the # of sig figs equal to the least # of sig figs in your problem

• 4.56 x 1.4 = 6.384• Round to 2 sig figs: 6.4

• For addition and subtraction, your answer should contain the # of decimal places equal to the least # of decimal places in your problem

• 12.11 + 18.0=30.11• Round to 1 dec place: 30.1

Dimensional Analysis• Dimensional analysis (DA) is the process we use to solve

many chemistry problems we will do throughout the year in our chemistry class (known as stoichiometry)• DA uses conversion factors and canceling out methodology to

derive the correct answer and unit

• We will practice it using metric conversion because they are familiar to you• If you simply solve the metric conversion using shortcuts you

have used in the past, you are missing the opportunity to practice the DA technique you will need when we tackle these more challenging scenarios later in the semester

• Keep at it! DA takes time and practice. You will get it if you are persistent and engaged as we work through our practice exercises available on School Loop.