MEASUREMENTS IN CHEMISTRY
Scientific 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 NOTATION
M 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.
801236.98

If the number is less than one you will have a
negative exponent and move the decimal to the
right.
-5
0.0000508

8.0123698 x 105
5.08 x 10
# of spaces moved by decimal = exponent
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.
8.0123698 x 105

If the exponent is negative you will have a small
number (<1) and move the decimal to the left.
5.08 x 10-5

801236.98
0.0000508
Exponent = # of spaces to be moved by decimal
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.
All nonzero numbers and zeros between are
significant.
1.
a.
909 cm, 1002 cm, 100,003 cm
Zeros at the beginning of a number are never
significant.
2.
a.
0.000912 cm, 0.01 cm, 0.000001001 cm
Zeros at the end of a number are significant only if
a decimal is present, and to the right of the decimal.
3.
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?