Working With Significant
Figures
Rule for Addition and Subtraction
For addition and subtraction, your answer must
show the same number of decimal places as the
number in the calculation with the least number
of decimal places.
Rule for Multiplication and Division
For multiplication and division, your answer
must show the same number of significant digits
as the measurement in the calculation with the
least number of significant digits.
Adding or Subtracting Significant
Figures
For example,
25.1 g + 2.03 g = 27.13 g
27.13 suggests that we can measure
with certainty to the hundreths place.
But the measurement of 25.1 says
we don’t know that value with
certainty to the hundredths place.
So we must round down to 27.1 g.
Multiplying or Dividing
Significant Figures
For example,
3.40 cm x 12.61 cm x 18.25 cm = 782.4505 cm3
before rounding
We, can’t report an answer with seven significant
digits if the measurement with the least number
of significant digits in our calculation, 3.40 cm,
shows only three significant digits. We must
round our answer to three significant digits,
giving us a rounded answer of 782 cm3.
Sample Problem
You weigh a metal chunk and it weighs 12.38 g
You drop it in a graduated cylinder with water and measure
a displacement of 8.26 ml
You use your calculator to get the density
Mass
D = Volume = 12.38 g / 8.26 ml
= 1.498789346 g/ml 10 sig. figs.
= 1.498 g/ml 4 sig. figs.
= 1.50 g/ml
3 sig. figs
Scientific Notation
• Number expressed as:
– Product of a number between 1 and 10 AND a power of 10
• 5.63 x 104, meaning
• 5.63 x 10 x 10 x 10 x 10
• or 5.63 x 10,000
• or 56,300
• 56.3 x 103 not standard scientific notation format
–
–
–
–
ALWAYS has only ONE nonzero digit to the left of the decimal point
ONLY significant numbers are used in the first number
First number can be positive or negative
Power of 10 can be positive or negative
When to Use Scientific Notation
• Astronomically Large Numbers
– mass of planets, distance between
stars
• Infinitesimally Small Numbers
– size of atoms, protons, electrons
• A number with “ambiguous” zeros
– 59,000 has two sig. figs.
– 5.9 x 104
Converting From Standard to
Scientific Notation
•
•
•
•
Move decimal until it is behind the first sig fig
Power of 10 is the # of spaces the decimal moved
Decimal moves to the left, the exponent is positive
Decimal moves to the right, the exponent is negative
– 428.5

4.285 x 102
(decimal moves 2 spots left)
– 0.0004285

4.285 x 10-4
(decimal moves 4 spots right)
Online Resources
•
•
•
•
•
Extra help with significant figures
Sig Fig help from the ScienceGeeks
Onlinemathlearning.com lesson on Sig. Figs.
Nice web page on metric system
Practice converting to scientific notation
Access to Mr. Dressen’s
Powerpoints