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Significant figures

It’s just a simple way to let the reader know – using the decimal system – how accurate our measurements are.

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Multiplying and Dividing

When multiplying or dividing, the # of sig figs should equal the least number of significant figures in any of the numbers used.

example:

1. 3.0 m (2 sig figs) x 4.67 m (3 sig figs) = 14 (2 significant figures)

2. 3000.0 km (5 sig figs) / 6.0 km (2 sig fig)

= 500 X *The answer cannot be 500 because it must only have 2 sig figs.

so we put it into scienctific notation

= 5.0 x 10 to the 2.

When adding or subtracting, the # of decimal places (not significant figures) in the answer should be the same as the least number of decimal places in any of the numbers used.

example:

1. 3.98 (2 decimal places) + 4.3 (1 decimal place) + 4.66565632 (8 decimal places) = 12.9 ( 1 decimal place)

2. 39.00 (2 decimal place) – 5.543 (3 decimal places) + 3.33 (2 decimal places) = 36.79 (1 decimal place)

* Even though it may seem tempting to make this answer 36.8, you CANNOT because you must have 2 decimal places according to the data that you received.

Note:

When doing multi-step calculations, keep at least one more significant figure in intermediate results than needed in your final answer!
For example: If your intermediate step gets you with 2 sig figs add a 3rd so there is no error at the end.

A Glossary of Frequently Misused or Misunderstood Physics Terms and Concepts.

Learning Standards

2016 Massachusetts Science Framework 2006

Physical Sciences (Chemistry and Physics) Grades 6-8

Recognize that the measurement of volume and mass requires understanding of the
sensitivity of measurement tools (e.g., rulers, graduated cylinders, balances) and
knowledge and appropriate use of significant digits.

The following skills are not detailed in the Mathematics Framework, but are necessary for a solid understanding in this course:
 Determine the correct number of significant figures.
 Determine percent error from experimental and accepted value