High school physic (significant figures )

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Significant Figures

The term significant figures actually refers to particular digits in a number. These are sometimes called significant digits. In this document we will use the term significant figures to discuss the broader topic. That way we may still say “digit” to draw your attention to a particular digit under discussion. After you have become familiar with the topic you may use either term.

Introducing Significant Figures

Only those figures or digits of a numerical quantity which are the result of actual measurement are said to be significant. For example, if you measure the thickness of a coin, you can write it as

1.6 mm or 0.16 cm or 0.0016 m.
How many significant figures are there in this measurement? Clearly only the digits 1 and 6 are the actual measured values. Therefore we have only 2 significant figures. Zeros used as placeholders are not significant. This would include all of the zeros in 0.0016 m.

We can use scientific notation to avoid misunderstanding. We would report the measurement as:
1.6 mm or 1.6 x 101 cm or 1.6 x 103 m.
With the use of scientific notation every digit that appears is significant. Here are some examples.

2.736 has 4 significant figures
2.00 has 3 significant figures
4 x 103 has 1 significant figure.
But 4.0 x 103 has 2 significant figures.
Standard notation would not let us distinguish between the last two examples. They would both appear as 4000.

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