Significant Figures and Exact Numbers
NO measurement is exact; some error is always involved
every answer in science has some uncertainty associated with it.
Significant Figures are the amount of digits that are accurate in a calculation.
The last digit of any measurement is an estimate - it is uncertain
The rules for determining how many significant digits are as follows:
All non-zero numbers are significant. (ie. 123 has three significant digits)
Zeroes at the end of a number that has no decimal point are not significant. (ie. 5000 has one significant digit)
When the number has portions before and after the decimal then all the numbers are significant. (ie. 1700.023 has seven significant digit).
In numbers that only have a decimal portion, zeroes at the beginning of the number do not count as significant. (ie. 0.000254 has three significant digits)
In Scientific Notation, significant digits are represented in the decimal number. (ie. 1.42 X 1012 has three significant digits)
Exact Numbers
Exact numbers, such as the number of people in a room, have an infinite number of significant figures.
Exact numbers are counting up how many of something are present, they are not measurements made with instruments.
There are exactly 12 inches in one foot.
if a number is exact, it DOES NOT affect the accuracy of a calculation nor the precision of the expression.
Examples:
There are 100 years in a century.
There are 12 eggs in 1 dozen eggs.