SIGNIFICANT FIGURES I:
Finding the significant digits in a number.
When we write a number we identify certain
digits as significant (meaningful or important)
and other digits as not significant because they
are simply placeholders for the decimal point.
The number of significant figures in a number is
directly tied to how precisely a number can be
determined. The more significant figures in a
number the more precise the number. Thus most
of the time we want to know how many significant
figures there are in a number.
SIGNIFICANT FIGURES I:
Finding the significant digits in a number.
Here are the three rules used to determine how
many digits in a number are significant.
1. All non-zero digits are significant.
2. Some zero’s are significant, others aren’t.
(More rules for this later)
3. Exact numbers or counting numbers have
infinite significant figures.
Let’s study the details
Rule 1:
All non-zero digits are significant.
A simple rule, here are some examples:
234.45 has 5 significant digits.
123,456,789 has 9 significant figures.
1.2 has 2 significant figures or digits.
Things get more interesting with zeros,
hence the next set of rules.
Rule 2:
Some zero’s are significant, others aren’t.
A. Leading zeros (.00045) are NOT significant.
B. Captured zeros (40005) ARE significant.
C. Trailing zeros….
…ARE significant when there is a decimal point.
450000.
…are NOT significant when there is no
decimal point.
450000
Practice with Rule 2:
Some zero’s are significant, others aren’t.
How many significant figures are there in the
following numbers? (Click for answer)
.405 ?
3 sig. fig. -- The 4 the 5, and the captured 0
.0405 ?
3 sig. fig. -- The leading zero doesn’t count
.0450 ?
3 sig. fig. Trailing zero counts because of decimal
450 ?
2 sig fig. No decimal so trailing zero doesn’t count
Rule 3: Exact or Counting numbers –
Infinite Sig. Fig.
Exact or counting numbers are numbers like
3 apples or 10 experiments or 18 atoms.
You always treat these numbers like they have
an infinite number of significant figures.
Exact numbers also occur in formulas like:
Volume of a sphere = 4/3 r3
(Both 3 and 4 can be treated as infinitely precise)
-or1 inch = 2.54 cm
(Both 1 and 2.54 can be treated as infinitely precise)
Practice Problems
Work your way through the following problems.
Practice Problems
How many significant figures are in the number
2.30500?
6 sig figs.
All nonzero digits are significant,
the captured or buried zero is significant,
and the trailing zeros are significant because
there is a decimal point in the number.
Practice Problems
How many significant figures are in the number
.005806?
4 sig figs.
All nonzero digits are significant,
the captured or buried zero is significant,
and leading zeros are never significant.
Practice Problems
How many significant figures are in the number
.0560?
3 sig figs.
All nonzero digits are significant,
, the leading zeros is not significant,
but the trailing zero is significant because
there is a decimal.
Practice Problems
How many significant figures are in the number
560?
2 sig figs.
All nonzero digits are significant,
the trailing zero is not significant
because there is no a decimal.