SIGNIFICANT FIGURES
Are they significant, or
“insignificant”?
SIGNIFICANT…
…means “important”
There is no such a thing as an “insignificant
figure”.
Digits that are not significant are called “nonsignificant digits”
RULES for determining which
figures are significant
1. Non-zero digits are always significant.
Ex: 0.0509
and
203,400.0
2. Trailing zeros to the right of the decimal point
are significant.
Ex: 0.0509
and
203,400.0
3. Zeros between non-zero digits are significant.
Ex: 0.0509
and
203,400.0
RULES (cont’d)
4. Zeros between non-zero digits and a decimal
point are significant.
Ex: 0.0509
and
203,400.0
5. Zeros used solely to place the decimal point
are not significant.
Ex: 0.0509
and
203,400.0
Answer: 0.0509 has 3 and 203,400.0 has 7 sig.
figs.
OPERATIONS with SIG. FIGS
There are two categories of operations with sig. figs
we will consider. Each has its own set of rules.
ADDITION/SUBTRACTION
MULTIPLICATION/DIVISION
Note: they are a simplification of the more general
rules to all operations, which are beyond the scope
of this course.
Addition/Subtraction Rule
• The final answer has the same number of
digits to the right of the decimal point as the
number with the smallest number of digits to
the right of the decimal point.
• Example:
97.3 + 5.85 = 103.15
97.3 has one digit after the decimal
5.85 has two digits after the decimal
answer = 103.2 (one digit after the decimal)
Note that both numbers have 3 sig. figs!
Multiplication/Division Rule
• The final answer must have the same number
of significant figures as the least precise
measurement – the one with the least
number of sig. figs.
• Example:
6.78 * 34 = 230.52
6.78 has 3 sig. figs
34 has 2 sig. figs
 answer = 230 (2 sig. figs)
THE END
Lilian Wehner ©