Transcript Significant Digits

Significant Digits
Rules for Significant Digits
1. All nonzero digits
are
significant
Example:
1,259.623
Significant
Digits: 7
Rules for Significant Digits
2. Zeroes
between nonzero digits
are
significant
Example:
1,009.6
Significant
Digits: 5
Rules for Significant Digits
3. Zeroes to Example:
the right of a 13.500
non-zero digit
are
significant
unless
otherwise
indicated
Significant
Digits: 5
Rules for Significant Digits
4 (a). A lone Example:
zero to the
0.558
left of the
decimal is not
significant
Significant
Digits: 3
Rules for Significant Digits
4 (b). Zeroes Example:
between the 0.005
decimal and
the first nonzero digit are
not
significant
Significant
Digits: 1
Do Not Confuse
Significant
Digits with
Decimal Places
Rule of Thumb: When
multiplying or dividing
measured numbers, the
result should have as
many digits as the
measured number with
the fewest digits.
Example:
10.500cm X 0.205cm = ?
The measured number with the
fewest digits is 0.205cm , so the
product should be rounded off
to 3 significant digits:
2
2.15cm
Example:
8.500g  4.50cm3 = ?
The measured number with the
fewest digits is 4.50cm3, so the
quotient should be rounded off to
3 significant digits:
1.89g/cm3
Sometimes Scientific
Notation is Required to
Express Products or
Quotients in the Correct
number of Significant Digits:
13.504g
3
 0.5cm =
3 X 101 g/cm3
?
When numbers are written in
scientific notation, the number
of significant digits is
expressed in the coefficient.
Example: 3 X 101 g/cm3
has one significant digit.
Rule for rounding: If a digit is 5
or more round the previous digit
up; otherwise leave the previous
digit at its value.
Examples: Round 3.89056 to 4
significant digits
3.891
Round 10.0649 to 4 significant
digits
10.06
If one is multiplying a measured
number by a counting number or π,
ignore the digits of the counting
number or π.
Example: Aluminum rods are 5.6cm
long. The total length of 7 rods
would be 7 X 5.6cm = 39cm (not
39.2cm). The product would be
rounded off to 2 digits as in 5.6cm.
To avoid a rounding off error during
multi-step calculations, round off the
answer at the end of the calculations
not at each intermediate step.
Example: A rectangular solid block
has a length of 8.89cm, a width of
2.61cm, and a height of 0.61cm. Its
mass is 5.329g. Its density would be
5.329g  (8.89cm X 2.61cm X 0.61cm) =
5.329g  14.153769cm3 = 0.38g/cm3
not 5.329g  14cm3