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.)

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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.
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.

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.


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?
804 005
300 403
quiz 2
Which digit in the number below is the estimated measurement?
900 004
60 409

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