significant figures

Significant Figures or Digits are the amount of digits that are accurate in a calculation. This is determined by how many digits there are in the numbers of the calculation. The rules for determing how many significant digits are as follows:
  • All non-zero numbers are significant.
  • Zeroes at the end of a number that has no decimal point are not significant. Ex. 500 only has one significant digit because the zeroes after the five do not count.
  • If a decimal point is placed after the last zero the zeroes do count as significant digits. Ex. 500. has three significant digits because the decimal point makes the zeroes significant.
  • When the number has portions before and after the decimal then all the numbers are significant. Ex. 1700.023 has seven significant digits.
  • In numbers that only have a decimal portion, zeroes at the beginning of the number do not count as significant. Ex. .00254 has three significant digits because the zeroes at the beginging of the number do not count.
  • In Scientific Notation, significant digits are represented in the decimal number. Such as, 1.42 X 1012 has three significant digits because there are three numbers in the decimal number that is multiplied by 10 to some power.*

rules for significant digits


* If you are not using Netscape, the numbers that are after the 10 in scientific notation are superscripts

The rules for determining the number of significant digits after a calculation are grouped by Addition and Subtaction, and Multipication and Division.

addtion and subtraction

When two or more numbers are added or subtracted the final answer is rounded off to the same decimal place as the number having its last significant digit the furthest to the left.

Example:
If you have the numbers 4.501 and 90.2 added together you will get 94.7 because the last column that both numbers use is the tenths place.

multiplication and division

Significant digits in Multipication and Division are determined by the number of significant digits in each of the numbers in the calculation. The answer must have the same amount of significant digits as the number in the calculation with the least amount of significant digits.

Example:
If you multiply the numbers 500 and 256 together the answer would be 100000 because 500 only has one significant digit so the answer can have only one significant digit. If you divide 1575 (four significant figures) by 17.6 (three significant figures), you round your answer to 89.5 (from 89.48863) so that it will have 3 significant digits.