Significant Figures Rules / Exercises

Introduction to Gen. Chem. Prof. K. Golestaneh, Copyright © 2010
Supplement B. Significant Figures in Math Operations and Uncertainty Page 1 of 4
Significant Figures Rules / Exercises
Write the number of significant figures (SF) above each number as
you read and understand the rules.
1. All non-zero digits (1-9) are to be counted as significant
including zero(s) between numbers (captive zeros).
178 905 10078 345 1.375 5.075
2. Zeros that make a number larger or smaller are not significant
(in precision). They are usually omitted from the number through
scientific notation. Write the scientific notation below each
number:
1750000 160800 0.000723 0.000000008107
Note: Zero to the left of a decimal (a number less than 1) is
never significant and often omitted. You do not have to enter it in
your calculator.
0.85 = .85 0.00375 = .00375
3. Zeros to the right of a decimal are always significant. Why?
These zeros do not have any impact on the value of the number
but make the number more or less precise. For example,
1.6 1.60 1.600 or 0.95 .950 0.9500
Note: You do not have to enter these zeros in your calculator.
How many SF are in: 4200 ??
If this number is exact? (i.e. exact number of people),
You would write it as: 4200 (exact)
it now has indefinite SF
What if it is an approximate vale (only good to 3 SF)?
You have no choice but to use scientific notation: 4.20 x 10 3
What if it is should be expressed to 4 SF?
You can use scientific notation _____________ or simply 4200.

Introduction to Gen. Chem. Prof. K. Golestaneh, Copyright © 2010
Supplement B. Significant Figures in Math Operations and Uncertainty Page 2 of 4
Note : Placing a decimal after these zeros will not change the value of
the number (you do not have to enter it in your calculator) but makes
the zeros captive and they count toward SF.
Example: Write 5000 to 2 SF ___________, 3 SF __________
4 SF ___________ or _____________ .
Rule For Expressing Proper Number Of Significant Digits In
Multiplication or Division
For multiplication and Division:
THE PRODUCT OR QUOTIENT WILL BE REPORTED AS HAVING AS MANY
SIGNIFICANT DIGITS AS THE NUMBER INVOLVED IN THE OPERATION
WITH THE LEAST NUMBER OF SIGNIFICANT DIGITS.
For example:
0.06001 x 230.80 = ___________
According to the indicated rule, the product should be expressed with
no more than _______ SF since 0.06001 has only _____ SF, while
230.80 has ____ SF.
1.87 x 10 5 / 7.500 x 10 -37 = ___________
The answer should be expressed with no more than _____ SF since the
lowest number of SF is ____ .
Example:
(2.0)(600.0) = ___________
Example:
(1.809)(14.0) (5.0 X 10 2 ) = ____________

Introduction to Gen. Chem. Prof. K. Golestaneh, Copyright © 2010
Supplement B. Significant Figures in Math Operations and Uncertainty Page 3 of 4
Rule For Expressing The Correct Number of Significant Figures in
Addition or Subtraction
This rule is considerably different than the one for multiplication or
division.
FOR ADDITION AND SUBTRACTION THE ANSWER MUST BE EXPRESSED
TO THE GREATER OF UNCERTAINTITIES.
What is uncertainty?
The lowest place significant digit of every number is always uncertain
by 1 unit. This means that the TRUE value of the number is somewhere
between the upper limit and lower limit expressed as :
Number ! uncertainty
For example :
1.07 ! 0.01 (since the least SF 7 is in the hundredths place)
650 _______
3000 ______
0.0820 _______
Now add and follow the indicated rule. Place the uncertainty above
each number before adding.
123.13 + 8.7 =
190.92 – 12.678 =
34000 + 1280 =
6700 + 12 =
17.123 + 9.0014 + 27.13

Introduction to Gen. Chem. Prof. K. Golestaneh, Copyright © 2010
Supplement B. Significant Figures in Math Operations and Uncertainty Page 4 of 4
Rules For Rounding Off Digits
How do we round off insignificant digits ?
1. If the least significant figure (LSF) is to the right of the decimal
and the digit that follows it is less than 5, simply eliminate all
digits to the right of the LSF.
2. If the LSF is to the right of the decimal and the digit that follows
it is greater than 5, add 1 to the LSF and then eliminate all digits
to the right of the LSF.
3. If the LSF is to the LEFT of the decimal and the digit that follows
it is less than 5, place zero(s) in place of all digits to the right of
the LSF.
For example if we wish to round off the following number to 3
significant digits:
17.382 ________
Round off 6.805 to three significant digits: __________
Another problem:
(6.75 x 7.5) + (2.79 x .017) =