Significant Figures and Scientific
Notation
Physics 11
• In both physics 11 and physics 12, we use
significant figures in our calculations.
• On tests, assignments, and labs students are
expected to answer questions with the correct
number of significant figures.
• Typically, 1 point on every assessment is given
directly to sig figs.
• Scientific notation is one way that scientists
show sig figs easily.
Sig Figs
• We have to look at significant figures because
the precision of all measuring devices is limited.
• Therefore, the number of digits that are valid is
also limited.
• The valid digits are called the significant digits.
- They are the digits you are sure of and one
estimated digit.
Sig Figs (Summary)
• We use significant figures to indicate the
PRECISION of the measuring tool.
• Significant figures indicate include all the
digits that can be directly measured and
one that is ESTIMATED.
Sig Figs (Summary)
•
RULES FOR DETERMINING HOW MANY SIG FIGS THERE ARE:
•
1. Nonzero digits are always significant.
Ex: 4.2
•
2. All final zeros after the decimal point are significant (if they are to the
right of a nonzero digit).
Ex: 4.200
•
4 sig figs
3. Zeros between two other significant digits are always significant.
(captive)
Ex: 4.02
•
2 sig figs
3 sig figs
4. Zeros used solely for spacing the decimal point are not significant. (place
holders) UNLESS THERE IS A DECIMAL AFTER
Ex: 4200
Ex: 4200.
2 sig figs
4 sig figs
Examples
•
•
•
•
•
•
•
•
1) 3.1428
2) 43.00
3) 0.40050
4) 0.00200
5) 302
6) 0.0056
7) 320
8) 320.
(5 sig figs)
(4 sig figs)
(5 sig figs)
(3 sig figs)
(3 sig figs)
(2 sig figs)
(2 sig figs)
(3 sig figs)
Scientific Notation (Summary)
• 1 digit before decimal (can’t be 0)
• Always ends with x10…
• If the exponent is positive, the number is LARGE
and vice versa
• The number of digits in a scientifically noted
measurement is the number of sig figs
Examples
• Change these from scientific notation into
regular number notation
– 5.6 x 104
– 1.9762 x 10-2
• Change these into scientific notation:
– 135.9 cm
– 0.89 m
Complete questions a, b, c on
Significant Digits Worksheet
Operations with Sig Figs
* the result of any mathematical operation
with measurements can never be more
precise than the least precise
measurement.
Addition and Subtraction
* Use the least number of decimals.
Multiplication and Division
• After performing the calculation, note the
factor with the least number of significant
figures. Round the answer to this number
of digits.
• 9.60 m ÷ 4.7632 s = 2.01545  2.02 m/s
From now on… (Summary)
• In physics, just use the rule:
– Sig Figs = least number of sig figs in the
question measurements.
– REMEMBER: If something is a constant or
counted, this is not included in sig fig
calculations.
– WHY?
– Don’t round until the end of the problem (keep
at least 4 decimals if you do need to round)
– Use the ANSWER button on your calculator
Complete side 2 of Sig Figs
Worksheet