Download Significant Digits and Uncertainty of Measurements

Significant Digits
Significant digits in measurements
and calculations
Significant Digits in Measurements

There are five rules or guidelines that
should be applied in determining whether a
digit in a measurement is significant.
Rule #1

Every nonzero digit in a measurement is
always significant.

Example: 24.7 m
3 significant digits
715.55 g
5 significant digits
Rule #2

Zeros appearing between nonzero digits
are significant.

Example:
7003 m
4 significant digits
1.503 g
4 significant digits
40.079 g
5 significant digits
Rule #3

Leading zeros are never significant. They
serve as placeholders only.

Example: 0.0071 m
2 significant digits
0.421 m
3 significant digits
0.000 099 m
2 significant digits
Rule #4

Trailing zeros are only significant if the
decimal point is written.

Example: 70 m
1 significant digit
70.0 m
3 significant digits
27, 000 cm
2 significant digits
Rule #5

Counting numbers and exactly defined
quantities have an unlimited number of
significant digits.

Example: 20 books
∞ number
1 hour = 60 minutes
∞ number
Review
How many significant digits are in each of
the following measurements?
a. 123 m
b. 0.123 m
c. 40.506 m
d. 98 00.0 m e. 22 metersticks f. 30 m
g. 0.07080 m h. 98 000 m

Significant Figures in Calculations

Calculated values must be rounded so that
they are consistent with the measurements
from which they were calculated.
Multiplication and Division


In calculations involving multiplication and
division, answers should be rounded so
that they contain the same number of
significant digits as the measurement with
the least number of significant digits.
Example: 7.55 m x 0.34 m =
2.4526 m / 8.4 m =
Addition and Subtraction


The answer to an addition or subtraction
calculation should be rounded to the same
number of decimal places (not digits) as
the measurement with the least number of
decimal places.
Example: 12.52 m + 349.0 m + 8.24 m =
74.626 m – 28.34 m =
Putting it All Together



Measure and calculate the length of the
perimeter of your note card. Round your
answer to the correct number of significant
digits.
Measure and calculate the area of your note
card (length x width). Round your answer to the
correct number of significant digits.
Calculate the number of minutes spent in school
in a 5 day week.
Question #1
 Form
a number that is
between 400 and 500
containing 2 significant digits.
Question #2
 Form
a number that is less
than 1, has 4 digits, and has
only 3 significant figures.
Question #3
 What
is the answer to the problem
63.4 x 14 rounded to the correct
number of significant digits?
Question #4
 What
is the answer to the problem
61.0 ÷ 9.1 rounded to the correct
number of significant digits?
Question #5
 What
is the answer to the problem
60 + 83.2 rounded to the correct
number of significant digits?
Question #6
 Form
a number that is greater
than 1000 having 6 significant
digits.
Question #7
 What
is the answer to the problem
0.158 + 0.4 rounded to the correct
number of significant digits?
Question #8
 Form
a number containing 3
zeros that has 4 significant
digits.
While waiting for the bell to ring,



Pick up handouts.
Get out note taking guide from yesterday
and complete the remaining problems as
review.
After completing the review problems, get
out the homework assigned yesterday and
identify any problems about which you
have questions.
How many significant digits are in each of the measurements below:
1) 100 m
2) 0.0230 m/s 3) 100.1 m
4) 2.0 x 1011 m/s 5) 50 metersticks 6) 10.380 s
Solve the following problems and round to the correct
number of significant digits.
7) 3.42 cm + 8.13 cm
8) 0.00457 cm x 0.18 cm
9) 85.0869 m2 ÷ 9.0049 m
10) 13.80 cm – 6.0741 cm
Write the following number in correct scientific
notation.
11) 0.00010500 µm