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JOURNAL #9

Determine each of the following to be a pure
substance, homogeneous mixture or a
heterogenous mixture:
Water
 Iron metal
 Sugar water

SCIENTIFIC
CALCULATIONSSIGNIFICANT FIGURES
TODAY’S LEARNING GOAL

Today, we will determine the amount of
significant figures in a given number.
WHAT IS THE LENGTH OF THIS LEAF?

(assume this ruler is measuring in cm)
 Significant
figures are critical when
reporting scientific data because
they give the reader an idea of how
well you could actually
measure/report your data
 Every
measurement has a degree of
uncertainty associated with it. The
uncertainty derives from the
measuring device and from the skill
of the person doing the measuring.
1.
ALL non-zero numbers
(1,2,3,4,5,6,7,8,9) are significant.
• 613 has three sig figs
• 123456 has six sig figs
2.
ALL zeroes between non-zero
numbers are significant.
• 5004 has four sig figs
• 602 has three sig figs
• 6000000000000002 has 16 sig
figs!
3. Trailing zeros are significant only if the
number contains a decimal point; otherwise they
are insignificant. Trailing zeros that aren't
needed to hold the decimal point are significant.
For example, 4.00 has three significant figures.
•
•
•
5.640 has four sig figs
120000. has six sig figs
120000 has two sig figs
4. Zeros to left of the first nonzero digit are
insignificant
•
•
•
0.000456 has three sig figs
0.052 has two sig figs
0.00000000000000000000000000052 also has two sig figs!
1.
2.
3.
4.
5.
6.
7.
8.
48,923
3.967
900.06
0.0004 (= 4 E-4)
8.1000
501.040
3,000,000 (= 3 E+6)
10.0 (= 1.00 E+1)
Number
# Significant Figures
Rule(s)
48,923
5
1
3.967
4
1
900.06
5
1,2,4
0.0004 (= 4 E-4)
1
1,4
8.1000
5
1,3
501.040
6
1,2,3,4
3,000,000 (= 3 E+6)
1
1
10.0 (= 1.00 E+1)
3
1,3,4
JOURNAL #7
Identify the number of significant figures for in
the problems below:
1. 456.23
2. .00025
3. 1.002
4. 236000
5. 1.023
6. 400
7. 4.5 x 10
8. 4.5
9. 30.1
10. 301
11. 3010

ADDITION AND SUBTRACTION WITH
SIGNIFICANT FIGURES
 When
combining measurements with
different degrees of accuracy and
precision, the accuracy of the final answer
can be no greater than the least accurate
measurement.
 When measurements are added or
subtracted, the answer can contain
no more decimal places than the least
accurate measurement.
EXAMPLE OF ADDITION/
SUBTRACTION
1. 7.939 + 6.26 + 11.1 = 25.299 (this is what
your calculator spits out)
• In this case, your final answer is limited
to one sig fig to the right of the decimal
• 25.3 (rounded up).
2. 150.0 + 1.507 = 151.5
ROUNDING OFF
 When
the answer to a calculation contains
too many significant figures, it must be
rounded off.
 There
are 10 digits that can occur in the
last decimal place in a calculation. One
way of rounding off
involves underestimating the answer for
five of these digits (0, 1, 2, 3, and 4)
and overestimating the answer for the
other five (5, 6, 7, 8, and 9).
ROUNDING OFF
 If
the digit is smaller than 5, drop this
digit and leave the remaining number
unchanged. Thus, 1.684 becomes 1.68.
 If
the digit is 5 or larger, drop this digit
and add 1 to the preceding digit. Thus,
1.247 becomes 1.25.
NOW IT’S YOUR TURN!
MULTIPLICATION AND DIVISION
WITH SIGNIFICANT FIGURES
The same principle governs the use of significant
figures in multiplication and division: the final
result can be no more accurate than the least
accurate measurement.
 In this case, however, we count the significant
figures in each measurement, not the number of
decimal places.
 When measurements are multiplied or
divided, the answer can contain no more
significant figures than the least accurate
measurement.

EXAMPLE
Calculate
the length in inches of
a piece of wood 1.245 feet long.
Determine the correct number of
significant figures.
 The
original measurement (1.254 feet) has four
significant figures, but there seem to be only two
significant figures in the number of inches in a
foot. Thus, it might seem that the answer should
contain only two significant figures.
 We
can clear up this confusion by remembering
that only measurements involve error or
uncertainty. Many unit factors are based on
definitions. For example, 1 foot is defined as
exactly 12 inches. Unit factors based on
definitions have an infinite number of significant
figures. The answer to this problem therefore
contains four significant figures.
EXAMPLE
 Calculate
the length in inches of a piece of
wood 1.245 feet long. Determine the
correct number of significant figures.
Answer:
14.94 in
NOW IT’S YOUR TURN!
Practice
for Quiz
on Friday!!!!