Significant Figures

Page 7

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

Rounding

A "5" rounds up to the next number unless two things are true... A "5" rounds down when

    1. There are no other numbers to its right or the numbers to the right are all zeros
    2. The number to the left of the five is an even number.
Examples

134.5 rounds to 134 when rounded to the one's place.
134.50 rounds to 134 when rounded to the one's place.
134.500 rounds to 134 when rounded to the one's place.
134.5000001 rounds to 135 when rounded to the one's place.
134.51 rounds to 135 when rounded to the one's place.
134.56 rounds to 135 when rounded to the one's place.
135.5 rounds to 136 when rounded to the one's place.
135.50 rounds to 136 when rounded to the one's place.
135.51 rounds to 136 when rounded to the one's place.

429.65 rounds to 429.6 when rounded to the tenths place.
429.650 rounds to 429.6 when rounded to the tenths place.
429.55 rounds to 429.6 when rounded to the tenths place.
249.75 rounds to 429.8 when rounded to the tenths place.

 

quiz
Round each number to the hundredths place following rounding rules of significant figures.
135.435
34.5655
20.4154
94.225
0.345
940.0051
0.98350001
140.3952
41.9950000
0.095500
31.9450000
8.935
Round each number to the 10's place following rounding rules of significant figures.
1255.032
165.001
25
145
235
395.1
294 385.000
15
565.1
105
645.008
894 395
816 375
828 935.25
835.22

 

Adding and Subtracting Significant Figures.

The concept to remember is when doing math, the answer is only as good as your worst estimate. Here a YouTube video explaining how to add numbers while following the rules of significant figures.

Summary

  • Line up the numbers to be added vertically.
  • Locate the significant figure farthest to the right for each number, this is the estimated measurement.
  • Add and subtract all the numbers without rounding any numbers -ever. Write down this answer.
  • Round the final answer to the place where the estimated number is farthest to the left.
 
quiz7
Simplify each expression while following the rules of significant figures.
23.4 + 0.450
34.5 - 2.34 + 8.2
10 + 12
34.67 - 3.45 + 0.99
8.34+ 0.234
132.4 + 12.5 - 61.4
34.0 + 345.0
234 - 90.0 + 12.5
34 - 8.2

14.56 + 102.3 - 4.007

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