MEASUREMENTS IN CHEMISTRYScientific Notation, Significant Figures, Percent Error

UNITS OF MEASUREMENT Put the following units in order from smallest

to largest. Meter, centimeter, millimeter, kilometer Kilogram, centigram, milligram, gram Liter, microliter, picoliter, kiloliter

SI UNITS

UNITS OF MEASUREMENT 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?

PREFIXES

SCIENTIFIC NOTATION 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

20oC 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 10n

SCIENTIFIC NOTATIONM x 10n

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 nth 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.

PRACTICE Convert the following from scientific notation

to their usual form. 6.39 x 10-4

3.275 x 10-2

8.019 x 10-6

PRACTICE Convert the following from scientific notation

to their usual form. 6.39 x 10-4 = 0.000639

3.275 x 102 = 327.5

8.019 x 10-6 = 0.000008019

PRACTICE Express the following numbers in scientific

notation. 843.4

0.00421

1.54

PRACTICE Express the following numbers in scientific

notation. 843.4 = 8.434 x 102

0.00421 = 4.21 x 10-3

1.54 = 1.54 or 1.54 x 100

SCIENTIFIC NOTATION CHEAT SHEET 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

801236.98

8.0123698 x 105

0.0000508

5.08 x 10-5

SCIENTIFIC NOTATION CHEAT SHEET 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

801236.98

8.0123698 x 105

0.0000508

5.08 x 10-5

SIGNIFICANT FIGURES If you were measuring this granite block in

inches, what would you determine its width to be?

SIGNIFICANT FIGURES In measurements there is always some

amount of uncertainty.

SIGNIFICANT FIGURES 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.

RULES FOR SIG FIGS 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. 0.000912 cm, 0.01 cm, 0.000001001 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, 900.0 cm

SIGNIFICANT FIGURES IN CALCULATIONS 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.

PERCENT ERROR 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 cm3 and the mass to be 562.5 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 cm3 and the mass to be 562.5 g.

Now look up the accepted value for the density of zinc in Table S on your reference tables.

A PROBLEM TO CONSIDER

Does your calculated value agree with the scientifically accepted value?

A PROBLEM TO CONSIDER

Does your calculated value agree with the scientifically accepted value?

A PROBLEM TO CONSIDER How “ far off ” is your calculated value from

the accepted value?

A PROBLEM TO CONSIDER How “ far off ” is your calculated value from

the accepted value?