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, "0.056" and NOT ".056."
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. |
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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. |
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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.
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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. |
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How many significant figures are in each number shown below? (Get a scrap piece of apaer and write your answer down befoe checking.) |
23.01 |
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6003 |
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409 |
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35.002 |
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804 005 |
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93821 |
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500.01 |
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300 403 |
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900.2 |
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508 |
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567 |
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30.0782 |
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Which digit in the number below is the estimated measurement? (Get a scrap piece of apaer and write your answer down befoe checking.) |
56.08 |
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35.02 |
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63.04 |
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30.006 |
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347.86 |
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900 004 |
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8907 |
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596 |
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60 409 |
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45 |
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