Significant Figures

Page 4
This text is meant to accompany class discussions. It is not everything there is to know about uniform circular motion. It is meant as a  prep for class. More detailed notes and examples are given in the class notes, presentations, and demonstrations (click here.)

Click for the questions that go with this reading

Counting the Number of Digits

The first thing that you need to know is how count the number of significant digits and how to find the estimated digit in a number.

So the explanations make sense, digits fit into one of two categories.
non-zero digits: 1, 2, 3, 4, 5, 6, 7, 8, 9
zeros: 0

Writing decimals.
When writing number less than zero, place a zero before the decimal place. This zero indicates that the dot on the paper is a decimal and not a random mark on the document. (It's not related to significant figures, it is point of style.) Three hundredths looks like this, "0.03" and not, ".03." Fifty-six thousandths looks like this, "0.0056" and NOT ".0056."

Numbers that are called "significant" are know with complete accuracy. It also understood that the last number in a string of significant figures is the estimated number.

In dealing with significant figures, a large part of identifying them is dealing with zeros. Here 6 rules to help deal with the role of zeros when counting and doing math operations with significant figures.

1. Non-zero numbers are all significant. The last number is the estimated measurement. The other numbers are known with exact precision.
 
Examples
432 3 sig. figs. 432:The 2 is estimated.
945.62 5 sig. figs. 945.62: The 2 is estimated.
58 341 5 sig. figs. 58 341: The 1 is estimated. The three zeros are significant.
245 379 6 sig. figs. 245 379: The 9 is estimated.
92.93817 7 sig. figs. 92.93817: The 7 is estimated.
685 721 394 9 sig. figs. 685 721 394: The 4 is estimated.
2.

Non-zero digits and zeros between non-zero digits are always significant.
In other words, zeros that are surrounded by non-zero numbers, are counted as significant.

In the number 2406, the 4 and the 6 are surrounding the 0. This make the zero significant. In the number 9380, the zero is not surrounded and is therefore no significant. Surrounding a zero by a non-zero number and a decimal on the RIGHT is the same as surrounding the zero by two non-zero numbers. "9380." means the zero is significant because of the number 8 on the left of the zero and the decimal is to the RIGHT. A decimal point to the left does not create significance. This is covered in a later rule.

 

 
Examples
501 3 sig. figs. 501:The 1 is estimated. The zero is between non-zero digits and it significant.
940.02 5 sig. figs. 940.02: The 2 is estimated. The two zeros significant too.
50 001 5 sig. figs. 50 001: The 1 is estimated. The three zeros are significant.
600 309 6 sig. figs. 600 309: The 9 is estimated. The zeros are all between other non-zero digits and are therefore significant.
62.03007 7 sig. figs. 62.03007: The 7 is estimated. The zeros are significant because they are between other non-zero digits.
3021 4 sig. figs.

3021: The 1 is estimated. The zero is significant.

60. 2 sig. figs. 60. : The 0 is estimated. The zero is surrounded by the 6 and the decimal ON THE RIGHT. -A decimal on the left does not count.
 
quiz 1
How many significant figures are in each number shown below?
23.01
6003
409
35.002
804 005
93821
500.01
300 403
900.2
508
567
30.0782
   
 
quiz 2
Which digit in the number below is the estimated measurement?
56.08
35.02
63.04
30.006
347.86
900 004
8907
596
60 409
45

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by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)