Significant figures

Significant figures

Author: Peter Anderson

1) to explain the need for significant figures, 2) teach how to count significant figures and 3) understand the difference between numbers that have significant figures and numbers that are exact.

What is so significant about them?

How many are there in this problem?

How many are there in this measurement?

Is everything a significant figure?

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The Atlantic Pacific approach

·       Atlantic (numbers without a period): Start counting from right with first significant figure (other than Zero).  Examples

1,207=  4

2050 =  3

 200  =  1


·        Pacific (numbers with a period): Start counting from left with first significant figure (other than Zero) and count All numbers to the right after the first.    Examples

2,076.9  = 5

   20.50  = 4

   0.020  =  2

Never fail flowchart with explanation



For those of you who enjoy flowcharts, this one covers the bases

Is the number defined or counted?

- Defined means set up by a ratio, such as 3:1.  Counted means counted.  The purpose of this step is to weed out numbers like 12 in a dozen or 2 in a pair.  The number of significant digits in these numbers doesn't factor in to the final count so they are classified as unlimited. 

- Numbers that aren't defined or counted are measurements from some sort of equipment.  In your labs, there are specific rules that are different from device to device for counting them.

- Numbers that aren't defined or counted are numbers from the problem.

Does the number have a decimal point?

- If it does there are specific rules in further steps.  If it doesn't . . .

Are trailing zeros present?

- Trailing zeros means numbers after the first nonzero number. 

- In 2,000,000 there is 1 significant digit, the 2.  The zeros are trailing zeros.

Are leading zeros present?

- Leading zeros means numbers between the decimal point and the first nonzero number.

- In 0.0000000035 there are 2 significant digits, the 3 and 5.  The zeros are leading zeros


Source: www.rpi.edu

The rules of significance

1.  Not a zero?  It's significant.

2.  Zero between two non zeros (Sandwich zero).  It's significant.        707      1001       2012

3.  Zero after a non zero and after a decimal point?  It's significant.  1.050    0.0530    200.00

4.  Counted or a conversion? It's infinitely significant.

Source: Peter Anderson

The rules of insignificance

1.  If a zero left is to the left of a nonzero?  It's insignificant.  This is called dangling left




2.  If a zero is to the right of a nonzero and before a decimal point?  It's insignificant.  This is called dangling right.




Source: Peter Anderson

Quiz yourself

Source: Peter Anderson