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Significant Digits

Significant digits allow scientists to express data to the required degree of accuracy.  Remember, the more decimal places a measurement has, the more accurate, or sensitive, the measurement is said to be.

Practice counting significant  digits:  significant digits practice worksheet

 

Rules for Counting Significant Digits

1. All non-zero numbers are significant.  (1, 2, 3, 4, 5, 6, 7, 8, 9, etc)

Example:  5.678 has four significant digits.

 

2. Zeros within a number are always significant.  (Zeros that are sandwiched.)

Example:  7.01 kilometers has three significant digits.

Example:  2005.307 has seven significant digits.

 

3. Zeros that do nothing but set the decimal point are not significant.  (Place holders)

Remember the trick, if you can write the number in scientific notation then the zeros are most likely place holders.  

Example:  100 has one significant digit.  (100 = 1 x 10^2  |   1 is the significant digit.)

Example:  0.0087 has two significant digits.  (0.0087 = 8.7 x 10^-3  |  8 and 7 are the significant digits.)

 

4. Trailing zeros that aren’t needed to hold the decimal point are significant.  (Zeros to the right of the decimal point)

Example: 7.0 has two significant digits.

Example:  3.15000 has six significant digits.

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Rules for Computing Significant Digits

 

Addition and Subtraction with Significant Digits

When measurements are added or subtracted, the answer can contain no more decimal places than the least accurate measurement.

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Multiplication and Division with Significant Digits

When measurements are multiplied or divided, the answer can contain no more significant figures than the least accurate measurement.

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SOURCE:

“Significant Figures.” General Chemistry Topic Review, Purdue University College of Science Chemical Education Division Groups. Web. June 13, 2013.

 

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