Chapter 2
Measurements and
Calculations
Quiz tomorrow
Dimensional Analysis
you must know base
units and prefixes!
Section 2-3
Using Scientific Measurements
Accuracy vs. Precision
Accuracy - refers to the closeness of
measurements to the correct or accepted
value of the quantity measured.
 Precision - refers to the closeness of a set of
measurements of the same quantity made in
the same way.

Accurate or Precise?
Percent Error
Calculated by subtracting the experimental value
(the value you find) from the accepted value
(“correct value”), dividing the difference by the
accepted value, and then multiplying by 100.
 % error = Value (accepted) - Value (experimental) x 100
Value (accepted)

Calculate the percent error in a length
measurement of 4.25 cm if the correct value is
4.08 cm
% error = 4.08 cm - 4.25 cm x 100
4.08 cm
% error = -4.2%
The % error has a negative value because the
accepted value is less than the experimental
value. If positive, the accepted value is
greater than the experimental value.
Significant Digits
(Also Called Significant Figures –
Abbreviated as sig. figs.)
Science almost always involves numbers.
 The numbers you use in math class are
exact numbers (they have infinite sig figs).
 In science, we use measurements, which are
NOT perfect numbers.
 It is important to recognize and report the
limitations of measurements along with the
magnitude and unit of the measurement.

Significant Figures
Sig figs are a system where the written
number indicates the limit of the
measurement.
 It is vital to include the zeros in your
measurement.

Sig figs (con’t)
These readings indicate the measuring
instrument had subdivisions down to the tenths
place and the hundredths place is estimated.
RULES FOR SIG FIGS





1. All nonzero digits are significant.
2. All zeros between non-zero digits are
significant.
3. All beginning zeros are NOT significant.
4. Ending zeros are significant if the decimal
point is actually written in but not significant if
the decimal is an “understood” decimal.
Zeros after nonzero digits after a decimal are
significant
RULES FOR ROUNDING
If digit following last
digit to be kept is:
Then the last digit
should:
Example (rounded to
3 sig figs)
Greater than 5
Be increased by 1
42.68 g → 42.7 g
Less than 5
Stay the same
17.32 m → 17.3 m
5, followed by nonzero
numbers
Be increased by 1
2.7851 cm → 2.79 cm
5, not followed by
nonzero digits and
preceded by odd #
Be increased by 1
4.635 kg → 4.64 kg
5, not followed by
nonzero digits and
preceded by even #
Stay the same
78.65 mL → 78.6 mL
Try the following:
How many significant figures are in each of
the following measurements? Based on
which rule?
 A. 28.6 g
 B. 3440. cm
 C. 910 m
 D. 0.046 04 L
 E. 0.006 700 0 kg

Adding or Subtracting with
Significant Figures
The answer for an addition or
subtraction problem must have digits no
further to the right than the shortest
added.
 Ex.

13.3843 cm
1.012 cm
+3.22 = 17.6163 = 17.62 cm
Multiplying or Dividing with
Significant Figures
For multiplication or division the answer
must have the same number of sig figs
as the factor with the least number of
sig figs.
 Example:
 (3.556 cm) (2.4 cm) = 8.5344 cm2
= 8.5 cm2

EXAMPLE PROBLEMS
A. 5.44 m – 2.6103 m = ?
 B. 2.4 g/mL x 15.82 mL
 C. What is the sum of 2.099 and
0.05681 g?
 D. Calculate the area of a crystal
surface that measures 1.34
micrometers by 0.7488 micrometers

Assignment
Significant Figures
Scientific Notation
Numbers written in scientific notation
follow the format M x 10n
 M = a number greater than or equal to 1 and
less than 10.
 n = any whole number.

For Example
To write the number 65 000 km (2 significant
figures) in scientific notation it would be
6.5 x 104 km
 M in this case is 6.5 (2 sig. figs.)
 n in this case is a positive value because
 65 000 is a large number.

Another Example
If you write a very small number in
scientific notation such as 0.000 12 mm, (2
sig. figs.) in scientific notation it would be
expressed as 1.2 x 10-4 mm.
 M in this case is 1.2 (2 sig. figs)
 N in this case is negative because 0.000 12
is a very small number.

Rules for writing in Scientific
Notation.
1. Determine M by moving the decimal point in the
original number to the left or right so that only one
nonzero digit remains to the left of the decimal
point. Keep all sig. figs.
 2. Determine n by counting the number of places
that you moved the decimal point. If you moved it
to the left, n is positive. If you moved it to the
right, n is negative.

A (Somewhat) Useful Mnemonic
Think of a registered
nurse carrying an oldfashioned record album
(an RN with an LP):
right = negative
left = positive

Assignment
2.3 Worksheet –
Due Tues. BOP
Working with Scientific
Notation – Due Wed. BOP