Monday, June 3, 2013

Calculations with Significant Figures

When combining measurements with different degrees of accuracy and precision, the accuracy of the final answer can be NO greater than the least accurate measurement.

KEEP IN MIND: Your answer CANNOT be more precise than the least precise measurement.


1. Addition and Subtraction with Significant Figures

The answer will have the same number of digits to the right of the decimal point as that of the least precise measurement.

For example,
1.25 + 2.589 = 3.839 = 3.84 (rounded up)

The least precise measurement (1.25) has 2 digits to the right of the decimal point. Thus, the final answer will have 2 digits to the right of the decimal point.

2. Multiplication and Division with Significant Figures

The number of significant figures in the answer will be the same as that of the measurement with the fewest number of significant figures.

For example,
2.36 x 1.764 = 4.16304 = 4.16 (rounded down)

The measurement with the fewest number of significant figures (2.36) has 3 significant figures. Thus, the final answer will have 3 significant figures.

3. Combination of Multiplication/Division and Addition/Subtraction

Apply the rules for Addition/Subtraction, followed by the rules for Multiplication/Division.

4. Conversion

The answer will have the same number of significant figures as that the number started with.

For example,
725 mmHg x (1 atm / 760 mmHg) = 0.953947368 = 0.954 atm

The number started with (725 mmHg) has 3 significant figures. Thus, the final answer will have 3 significant figures.

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