Scientific Notation and Significant
Figures
Dr. MJ Patterson
This section will look at applying the rules for sig figs to a number written in scientific notation. It is fairly simple. All of the digits in the base are significant. The numbers in the exponent are not significant.
Keep in mind that any part of the number that merely serves as a decimal placeholder is not significant. That immediately rules out the exponent, because it just tells you how many places to move the decimal point.
Example 1:
In each of the following numbers, underline all of the significant digits, and
give the total number of significant digits.
a. 6.02 x 1023
b. 1.6 x 10-19
c. 5.0 x 10-3
Solution 1:
a. 6.02 x 1023 - all the numbers in the
base are significant, including the sandwiched zero - 3 sig figs
b. 1.6 x 10-19 - all the
numbers in the base are significant - 2 sig figs
c. 5.0 x 10-3 - all the numbers in
the base are significant , including the zero to the right of the number and
the decimal (if it were not significant, it just would not be there) - 2 sig
figs
Example 2:
Write the following numbers using conventional notation.
a. 5.0 x 10-3
b. 5.0 x 103
Solution 2:
a. 0.0050 - the zero must be written at the end to keep the
same number of sig figs
b. 5000 - the first zero must
be underlined to indicate that it is significant