Significant Figures/Significant Digits
(a.k.a. Sig-Figs or Sig-Digs)
There are two types of numbers: exact and inexact.
Exact numbers are counting numbers or defined quantities.
Ex. 12 eggs = 1 dozen
There are 26 letters in the alphabet.
EXACT NUMBERS ARE NOT TO BE CONSIDERED IN DETERMING
THE NUMBER OF SIGNIFICANT DIGITS FOR A CALCULATION.
Inexact numbers are based on measurements.
Ex. A person’s mass on a certain scale is 62.78 kg.
The thickness of a certain sheet of metal is 1.23 mm.
These measurements are inexact because the precision using a
different type of instrument will influence the reading.
A person’s mass can be 63 kg, or 62.783 kg
An instrument can read, 1.2 mm or 1.234 mm.
The last digit in any measurement is an estimation, while
all other digits proceeding the last digit are known quantities.
Significant Figure Rules
1) Non-zero numbers are always significant.
2) Zeroes between two significant figures are always significant.
Ex. 90.007 kg
1.0046 L
3) All zeroes after both a significant figure and a decimal point are
significant.
Ex. 24.000 m
936.0400 g
4) Leading zeroes are not significant.
Ex. .000483 m
.0791 kg
5) Trailing zeroes in integers with no decimal point are not
significant?
Ex. 230,000 years
-400 cm/s
*How many significant figures are in each of the following?
a) 803 m b) .0004050 kg
c) 23.040?
d) 750,000
Accuracy/Precision
• Accuracy: Closeness of a measurement to the
standard value or accepted value of that
quantity.
• Precision: Degree of exactness of a
measurement.
•  = 3.14
• Accurate numbers to : 3.12, 3.17, 3.16, 3.13,
3.15
• Precise numbers to : 3.142, 3.1416, 3.14159,
3.141593
In measurements, precision refers to the how closely each measurement
agrees.
Ex.: 2.34 cm, 2.33 cm, 2.32 cm are precise measurements because they
closely agree to each other with only ±0.01 cm deviation from the average.
Significant Figures Arithmetic
Addition/Subtraction:
Use the same number of decimal places as the
least precise number in the calculations.
30.532 m
9.8 m
the least precise number with one decimal place
+
11.86 m
-----------------52.192 m
• Ans: 52.2 m the same number of decimal
places as the least precise number in the
calculation
Exceptions
7.000x103 m
+ 1.0 x102 m
-----------------7.1 x103 m
Not the correct precision
7.000x103 m
+
.10 x103 m
------------------
The smaller number must be converted to same
power of ten as the larger number and then the
precision can be compared.
7.10 x 103 m answer
Another example of the exception
4.0 x 103 mL
+ 1 x10-2 mL
------------------
4.0
x 103 mL
+
.00001 x103 mL
-----------------4.0 x 103 mL answer
Multiplication/Division
• Use the same number of significant figures as
the number with the smallest number of
significant figures.
•
60.49 m
 14.07 m/s
4.3 s
• Answer: 14 m/s
• Since 4.3 s has the least number of significant
figures between the two numbers, the answer
will be expressed with two significant figures.