Significant Figures

Page 5
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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More Significant Figure Rules

3.

Leading zeros before the first non-zero digit are not significant. These leading zeros are called "placeholders." They slide the other number around. In doing so they show how small the other number are. For example 3 hundredths is written 0.003. The "0." is used to highlight the decimal. The, "00," to the left of the number 3 is showing how small the number3 is. This rule is only for numbers less than 1.

 

 
Examples

The zeros that are placeholders are highlighted in yellow.

0.03895 4 sig. figs.
0.03895 are the significant figures. The 5 is the estimated measurement.
0.00452 3 sig. figs. 0.00452: The 2 is the estimated measurement.
0.0006 1 sig. fig. 0.0006: The 6 is estimated measurement.
0.0456 3 sig. figs. 0.0456: The 6 is estimated measurement.
0.0000024 2 sig. figs. 0.0000024: The 4 is estimated measurement.
0.006005 4 sig. figs.
0.006005: The 5 is estimated measurement. The two zeros highlighted in pink are bookended by non-zero numbers and are therefore significant too and not a placeholder.
0.0050678 5 sig figs.
0.00506758: The 8 is estimated measurement. The zero between the 5 and the 6 is bookended by two non-zero number and is therefore significant and not a placeholder.
4.

Trailing zeros to the right of the decimal point are always significant.
Compare two measurements, 30 centimeters and 30.00 centimeters. Both of there numbers convey 30 centimeters. But the extra zeros on 30.00 mean that the measurement estimated to hundredths place. In other-words it was made using a ruler where the distance could be estimated between the millimeter marks. This ruler would look like the one below.

The, "3," in, "30," centimeters is an estimated number, this means that the ruler that made this measurement was marked every 10 cm. It could have looked like the one below.

The zeros after the 30 in 30.00 do not need to be there ti convey 30 centimeters. But the fact that they are there means that the measure was made by using a ruler with many small markings and thus a higher precision. Because they are not needed but are added, means they are significant.

 
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.

 

 
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

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