- ABSOLUTE VALUE:
The symbol for "absolute value" is two vertical bars: | x |
The absolute value of a positive number (or zero) is the same as the number.
The absolute value of a negative number is the number with the sign changed to + (positive).
The absolute value of a difference is always the larger number minus the smaller one.
- PERCENT ERROR:
Percent error = __ _ | Measured value - Accepted value | _ __ x 100%
Accepted value
- The numerator of the fraction above is an absolute value, so it's always positive. You can always
subtract the smaller number from the larger one.
- Notice that the numerator of the fraction above is usually small compared to the denominator,
so the fraction will be a small number. That's why it's multiplied by 100%.
- Units: Notice that the Measured value and the Accepted value are in the same units,
whatever they are, so that the numerator and denominator of the fraction are both in the
same units. The units therefore cancel out, so that the percent error is a
"dimensionless" number without any units.
- SAMPLE PROBLEM:
If the measured value is 7.7 cm and the accepted value is 8.0 cm, find the percent error.
ANSWER: Percent error = ( | 8.0 cm - 7.7 cm | / 8.0 cm ) x 100%
= ( 0.3 cm / 8.0 cm ) x 100% = .0375 x 100% = 3.75%
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