Download Significant Figures

Spring 2001
MCCORD — CH304K
page 1
Scientific Notation and Significant Figures
Scientific Notation: Any number can be represented in the following form:
#.## x 10**
The first part of the number with the decimal point (#.##) is called the mantissa and the
other number (**) is known as the exponent. Try these conversions:
number
0.0000323
4000
65 million
0.000000012
scientific notation
3.23 x 10-5
4. x 103
6.5 x 107
1.2 x 10-8
To enter a number in scientific notation on your calculator do the following:
Example: enter 5.023 x 10-8 on your calculator.
First:
enter the mantissa, press "5.023"
Second: enter the exponent mode, press the "EE" key or on some
calculators the "EXP" key.
Third:
now enter the exponent, press "-8" or you can enter "8-" the sign can be
entered before or after the exponent on most calculators.
Your calculator should be displaying something like:
_ _ _ _ 5.023_-08_
Significant figures (or digits) are made up of a series of certain digits plus ONE
uncertain digit. In the examples below the uncertain digit is shown in bold. Note however
that it IS significant. Remember that leading zeros are not significant, inside and trailing
zeros are significant.
number
10.2
4.003
12.34098
6.0000
sig figs
3
4
7
5
number
0013.50
1 x 10-4
2.34 x 1019
6.0 x 104
sig figs
4
1
3
2
The rule for counting significant figures for decimal numbers is to start counting with the
first non-zero digit and count the rest of the digits shown. When counting significant
figures for scientific notation numbers, only the mantissa is counted, not the exponent.
For counting numbers (usually reported as an integer with no decimal), the number of
significant figures is infinite (sig figs = ∞). If you have 13 donuts you know that is exact
and isn't ±0.1 donut. You must then use your discretion when dealing with large integer
numbers. If someone tells you they make $25,000 per year, is that exact? Probably not,
and you might say that number has only 2 sig figs, the "2" and the "5". The 3 zeros just
establish that it is 25 thousand. Trailing zeros on integer numbers may or may not be
significant. Look at the context in which they are used and decide on the right number.
Spring 2001
MCCORD — CH304K
page 2
Adding and subtracting numbers
The rule is to keep track of where the first uncertain digit is and report no further than
that. Uncertain digits shown in bold.
12.34
sf = 4
10.2
sf = 3
0.2
sf = 1
9.2380 sf = 4
31.9780 ------------> report as 32.0 (3 sig figs)
rounded to nearest tenth
Multiplying and dividing numbers
The rule is to report the answer with the same number of significant figures as the least
significant number in the calculation. Uncertain digits shown in bold.
2.45 x 1.245 x
2.7 =
8.235675 ---------> report as 8.2
Note that the three numbers given here each have a different number of significant
figures (3, 4, and 2 respectfully). The answer must be reported with only 2 significant
figures.
Rules for extended calculations
Work the entire problem as if every number was very significant (sig figs = ∞). Do not
round-off any intermediate numbers. Wait till you get your final answer and then report
the number with the correct number of significant figures (rounding as appropriate).
NOTE: For numerical problems on our bubble sheets, you MUST bubble 3 significant
digits in the mantissa regardless of the way the question reads. This is not scientifically
correct, it's just necessary for the computer to grade you properly. Usually you will be
given a ±2% tolerance on your answer anyway. Also note that you must bubble 2 digits
for the exponent term, a leading zero will be necessary if the exponent is a single digit
number.