Questions and Answers
When performing calculations involving significant figures, what common mistake do students often make, and how can using significant figure rules help?
Students often keep too few figures by rounding off too much and lose information, or they keep too many figures by writing down whatever the calculator displays. Using significant figure rules helps us express values with a reasonable degree of precision.
What is the rule for retaining significant figures when multiplying or dividing, and why is this rule important?
The number of significant figures retained may not exceed the least number of digits in either of the factors. This rule is important because it ensures that the product or quotient has a reasonable degree of precision.
When adding or subtracting measurements with different numbers of decimal places, how should the result be expressed?
The result should be expressed to the same number of decimal places as the measurement with the least number of decimal places.
What is the purpose of placeholder zeroes in a measurement, and how do they affect the number of significant figures?
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When expressing a quotient, how should the answer be rounded, and why?
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Study Notes
Significant Figures Rules
- When a decimal point is not explicitly expressed, zeroes following the last non-zero digit are not significant, they are place holders only.
- Zeroes preceding the first non-zero digit are not significant, they are place holders only.
Retaining Significant Figures
- Retain all digits that are certain of plus one estimated digit.
- For example, in the measurement series
to = 20.78 s,t1 = 20.32 s,t2 = 20.44 s, ..., retain two significant figures (tens and units).
Rules for Addition and Subtraction
- Change the units of all measurements to the same units.
- The sum or difference of measurements may have no more decimal places than the least number of places in any measurement.
Rules for Zeros
- All non-zero digits in a measurement are considered significant.
- Zeroes are significant if bounded by non-zero digits.
- If a decimal point is expressed, all zeroes following non-zero digits are significant.
Rules for Multiplication and Division
- When multiplying or dividing, the number of significant figures retained may not exceed the least number of digits in either factor.
- Example:
0.304 cm x 73.84168 cmhas only three significant figures because one of the factors has only three significant figures, therefore the product can have only three.
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Description
This quiz covers the rules of significant figures in measurements, including decimal points and zeroes as place holders. It also provides an example of calculating the average of a series of measurements.
