Significant Digits
Calculations involving measured figures must always take into consideration the precision of those measurements.  All digits which are actually part of a measurement are known as significant figures. Those which serve some other function, as in acting as a place-holder, are not significant. It follows that all non-zero digits recorded in a measurement are significant.  Zeros may or may not be significant depending on their function.  Zeros which have been measured are significant.  Those that act as place-holder are not.  The solved examples below  illustrate the ways in which one can determine if a zero is significant or not.

Significant digits must be taken into consideration in determining the correct answer to a calculation involving measured digits.  Two rules apply.

Precision Rule:  During an addition or subtraction the answer can have no more decimal places than the value with the least number of decimal places.

E.g..   4.55 + 6.334 + 9.1 = 19.984 = 20.0   (The answer can have only one decimal place because 9.1 had only 1 decimal place)

Certainty Rule: During a multiplication or division the answer can have no more significant digits than the value with the least number of significant digits.

E.g..  3.55 X 6.3333 = 22.483215 = 22.5
Example_1 How many significant digits are there in the number 307 cm?
Solution:
Both the first and last digits (3 and 7) are non-zero, so they are both significant.  Since the zero lies between two significant digits, it must also be significant.  The answer, therefore, is three.


Example_2
How many significant digits are there in 0.00450 cm?
Solution:
The first three zeros are not part of the measurement.  They are place-holders here.  The two non-zero digits (4 and 5) are both significant.  The final zero does NOT serve as a place-holder. It must be significant also.  Therefore this number has three significant digits.


Example_3
What is the sum of 4.52 g, 13.8 g and 7.9483 g?
Solution
adding these three numbers gives and answer of 26.2683 g.  The least accurate number among the numbers used in the addition is 13.8 g. Therefore the answer can have no more than 1 decimal place of accuracy, hence the answer is 26.3 g


Example_4
What is the product of 48.4398 m and 1.52 m?
Solution
Multiplying these gives an answer of 73.628496 m2.   The number of significant figures in the two numbers used in the multiplication are 6 and 3 respectively.  Therefore the answer can only have 3 significant digits.  Hence the answer is 73.6 m2.


Significant Digits Practice Level 1
Significant Digits Practice Level 2
Significant Digits Practice Level 3