Formulas/Worded
What is "Precision" in terms of error in measurement?
"Precision" is the smallest unit on the measuring instrument.
If the relative error of a measurement is 0.03, what is the percentage error?
Percentage error
= 0.03 x 100%
= 3%
If:
Actual Value= 2.57kg
and the Measured Value= 2.5kg,
What is the 'Absolute Error?'
Absolute error = measured value - actual value
2.5kg-2.57kg
= - 0.07kg or - 70grams
How do you calculate upper and lower bounds for given measurements?
Measurement (+/-) the absolute error.
What is 'absolute error' and how is it calculated?
Absolute error is the difference between the actual value and measured value. OR it is half the precision.
Absolute Error= Actual Value - Measured Value
If absolute error = 0.015kg and actual value= 2.467kg, calculate the relative error to 3 decimal places.
Relative error= 0.006
On a 30cm ruler, the smallest unit of measurement is 1mm. Hence, what is the absolute error?
Absolute error= +/- 0.5mm
A pencil case is measured to be 25cm long and the absolute error is 0.5cm. What is the upper bound?
Upper bound= 25cm+0.5cm
= 25.5cm
What is the difference between 'relative error' and 'percentage error?'
How they are expressed.
Relative error=decimal
Percentage error= written as a percentage
The previous question had a relative error of 0.006, what would the percentage error be for that measurement?
Percentage Error= 0.6%
The smallest unit of measurement on a stopwatch is 0.05 seconds. Hence, what is the absolute error?
Absolute error = +/- 0.025 seconds
If the precision of a measurement instrument is 5cm, what valued is used in order to find the upper/lower bounds?
5cm divided by 2= 2.5cm. It is then added/subtracted from the actual measurement.
How are the upper/lower bounds of a measurement calculated?
Measurement (+/-) the absolute error
Calculate the percentage error if the actual value of a measurement is 3.752cm and the absolute error is 0.014mm. Answer to 2 decimal places.
Percentage error
= (0.014/3.752) x 100
=0.37%
If the actual weight of a bag of grapes is 457 grams, but the recorded weight is 450 grams, what is the absolute error?
Absolute error = measured value - actual value
= 450g - 457g
= - 7g
Explain what is meant by 'the upper and lower bounds' of a measurement?
The highest and lowest possible values a measurement could take. The upper and lower ends of the range a measurement could be.
Name a possible source of error when using measuring instruments.
The possible sources of errors include mistakes in reading the scale, parallax error and calibration error
If the percentage error of a measurement is 0.7258%, what is the relative error, to 5 decimal places?
Relative Error= 0.00726
On a clock, the smallest unit of measurement is 1 second. True or false, the absolute error of this clock is +/- 1 second. Why or why not?
Answer: False, because the absolute error is half the precision and hence is +/- 0.5 seconds.
If a book is measured to be 27cm long, to the nearest cm, calculate the upper and lower bounds.
Precision= 1 cm
Absolute error = +/- 0.5 cm
Upper Bound= 27.5cm
Lower Bound= 26.5cm