M EASUREMENTS IN C HEMISTRY Scientific Notation, Significant Figures, Percent Error

U NITS OF M EASUREMENT Put the following units in order from smallest to largest. Meter, centimeter, millimeter, kilometer Kilogram, centigram, milligram, gram Liter, microliter, picoliter, kiloliter

SI U NITS

U NITS OF M EASUREMENT Put the following units in order from smallest to largest. millimeter, centimeter, meter, kilometer milligram, centigram, gram, kilogram picoliter, microliter, liter, kiloliter What information do the prefixes centi, milli, kilo, etc. provide?

P REFIXES

S CIENTIFIC N OTATION When studying chemistry it is common to encounter very large or very small numbers. Need a system in which to shorten long number chains. Ex: The number of air molecules in a liter of air at 20 o C and normal barometric pressure is 25,000,000,000,000,000,000,000. Ex: The distance between two hydrogen atoms in a diatomic hydrogen molecule is 0.000,000,000,074 meters. In Scientific Notation, these long chains of numbers are written in the form of; M x 10 n

S CIENTIFIC N OTATION M x 10 n Scientific notation is simply a number time 10 raised to an exponent. M is a number greater than or equal to 1 and less than 10. n is the exponent (the n th power or 10). It can be either positive or negative and represent the number of decimal places moved. Positive (+) n means a large number so the decimal moves to the right by n places. Negative (-) n means a small number so the decimal moves to the left by n places.

P RACTICE Convert the following from scientific notation to their usual form x x x 10 -6

P RACTICE Convert the following from scientific notation to their usual form x = x 10 2 = x =

P RACTICE Express the following numbers in scientific notation

P RACTICE Express the following numbers in scientific notation = x = 4.21 x = 1.54 or 1.54 x 10 0

S CIENTIFIC N OTATION C HEAT S HEET When converting from standard notation to scientific notation… If the number is one or greater you will have a positive exponent and move the decimal to the left. If the number is less than one you will have a negative exponent and move the decimal to the right. # of spaces moved by decimal = exponent x x 10 -5

S CIENTIFIC N OTATION C HEAT S HEET When converting from scientific notation to standard notation… If the exponent is positive you will have a large number (>1) and move the decimal to the right. If the exponent is negative you will have a small number (<1) and move the decimal to the left. Exponent = # of spaces to be moved by decimal x x 10 -5

S IGNIFICANT F IGURES If you were measuring this granite block in inches, what would you determine its width to be?

S IGNIFICANT FIGURES In measurements there is always some amount of uncertainty.

S IGNIFICANT F IGURES Repeating a particular measurement will usually not obtain precisely the same result. The measured values vary slightly from one another. Precision – refers to the closeness of a set of values obtained from identical measurements of something. Accuracy – refers to the closeness of a single measurement to its true value.

R ULES FOR S IG F IGS The number of digits reported for the value of a measured quantity. 1. All nonzero numbers and zeros between are significant. a. 909 cm, 1002 cm, 100,003 cm 2. Zeros at the beginning of a number are never significant. a cm, 0.01 cm, cm 3. Zeros at the end of a number are significant only if a decimal is present, and to the right of the decimal. a. 900 cm, cm

S IGNIFICANT F IGURES IN C ALCULATIONS Multiplication and Division The answer is given with as many significant figures in the measurement with the least amount of significant figures. Addition and Subtraction The answer is given with as many significant figures as the measurement with the least number of decimal places.

P ERCENT E RROR Sometimes it is important to calculate how far off a measured value has deviated from the true or accepted value. For this we use Percent (%) Error.

A PROBLEM TO CONSIDER A student measures the volume of a piece of zinc, by water displacement, to be 75.0 cm 3 and the mass to be g. Now look up the accepted value for the density of zinc in Table S on your reference tables.

A PROBLEM TO CONSIDER A student measures the volume of a piece of zinc, by water displacement, to be 75.0 cm 3 and the mass to be g. Now look up the accepted value for the density of zinc in Table S on your reference tables.

A P ROBLEM TO CONSIDER Does your calculated value agree with the scientifically accepted value?

A P ROBLEM TO CONSIDER Does your calculated value agree with the scientifically accepted value?

A P ROBLEM TO CONSIDER How “ far off ” is your calculated value from the accepted value?

A P ROBLEM TO CONSIDER How “ far off ” is your calculated value from the accepted value?