Summing It All Up
- Every measurement has some uncertainty in it; reported values should not
contain unknown information
- When making a measurement with a device having a marked scale (like a ruler,
a dial, or a non-digital watch), always estimate the value one degree of accuracy
beyond the scale of your measurement device.
- The last digit you report should be the first digit with uncertainty in
it.
- These digits we are reasonably certain about (including the one with some
uncertainty) are the significant figures, also called significant
digits.
- Significant digits are identified by following a few conventions:
- Any non-zero digit in a reported number is significant.
- If a zero is found between significant digits,
it is significant.
- Zeros to the right of the decimal place that
are NOT merely place holders are significant; these significant zeros will
be to the right of non-zero significant digits.
- Conventions about zeros at the end of a number
and to the left of the decimal place vary. In these modules, such zeros
will always be considered insignificant. You should, however, look in your
textbook to determine that author's convention.
- When a whole number is known exactly, it can
be treated as having an infinite number of significant figures even when
the zeros are not written out.
- The uncertainty in a calculated value is determined
by the uncertainty of the least certain original number.
- When multiplying or dividing two or more numbers,
count the significant figures in each of the original numbers. Take the
smallest of the numbers of significant figures. The product or quotient
will have that minimum number of significant figures.
- When adding or subtracting two or more numbers,
the last significant digit is the digit in the rightmost decimal place common
to all the original numbers.
- When using numbers in calculations, it's a good
idea to keep one digit beyond the significant digits. Once the final answer
is calculated, it may be expressed with the correct number of significant
digits.
- Several of these conventions are summarized in a helpful flow
chart.
Test your knowledge now by taking the quiz for this module.
Copyright © 1999 Rensselaer Polytechnic Institute
and DJ Wagner. All Rights Reserved.