He Percentage error Is the manifestation of a relative error in percentage terms. In other words, it is a numerical error expressed by the value that gives a relative error, later multiplied by 100 (Iowa, 2017).
To understand what a percentage error is, first it is crucial to understand what a numerical error is, an absolute error, and a relative error, since the percentage error is derived from these two terms (Hurtado & Sanchez, s.f.).
A numerical error is one that occurs when a measurement is taken equivocally when using an apparatus (direct measurement), or when a mathematical formula (indirect measurement) is misapplied.
All numerical errors can be expressed in an absolute or percentage way (Helmenstine, 2017).
For its part, the absolute error is that which is derived by making an approximation to represent a mathematical quantity resulting from the measurement of an element or from the erroneous application of a formula.
In this way, the exact mathematical value is altered by the approximation. The calculation of the absolute error is done by subtracting the approximation to the exact mathematical value, thus:
Absolute Error = Exact Result - Approximation.
The units of measure used to manifest the relative error are the same ones used to speak of the numerical error. In the same way, this error can give a positive or negative value.
The relative error is the quotient obtained by dividing the absolute error between the exact mathematical value.
In this way, the percentage error is that obtained by multiplying the result of the relative error by 100. In other words, the percentage error is the percentage expression (%) of the relative error.
Relative Error = (Absolute Error / Exact Result)
A percentage value that can be negative or positive, that is, it can be a value represented by excess or default. This value, unlike the absolute error, does not present units, beyond those of the percentage (%) (Lefers, 2004).
Relative Error = (Absolute Error / Exact Result) x 100%
The mission of relative and percentage errors is to indicate the quality of something, or to provide comparative value (Fun, 2014).
Examples of percent error calculation
1 - Measurement of two land
When measuring two lots or lots, it is said that there is approximately 1 m error in the measurement. One plot is 300 meters and another plot is 2000 meters.
In this case, the relative error of the first measurement will be greater than that of the second, since in proportion 1 m represents a greater percentage in this case.
Lot of 300 m:
Ep = (1/300) x 100%
Ep = 0.33%
Lot of 2000 m:
Ep = (1/2000) x 100%
Ep = 0.05%
2 - Aluminum Measurement
In a laboratory an aluminum block is delivered. When measuring the dimensions of the block and calculating its mass and volume, the density of the block (2.68 g / cm3) is determined.
However, when reviewing the numerical table of the material, this indicates that the density of the aluminum is of 2.7 g / cm3. In this way, the absolute and percentage error would be calculated as follows:
Ea = 2.7 - 2.68
Ea = 0.02 g / cm 3.
Ep = (0.02 / 2.7) x 100%
Ep = 0.74%
3 - Attendees to an Event
It was assumed that 1,000,000 people would attend a given event. However, the exact number of people who attended the event was 88,000. The absolute and percentage error would be the following:
Ea = 1,000,000 - 88,000
Ea = 912,000
Ep = (912,000 / 1,000,000) x 100
Ep = 91.2%
4 - Ball Drop
The time that is calculated must take a ball to reach the ground after being thrown at a distance of 4 meters, is 3 seconds.
However, at the time of experimentation, it is discovered that the ball took 2.1 seconds to reach the ground.
Ea = 3 - 2.1
Ea = 0.9 seconds
Ep = (0.9 / 2.1) x 100
Ep = 42.8%
5 - Time it takes a car to arrive
It is estimated that if a car goes 60 km, it will reach its destination in 1 hour. However, in real life, the car took 1.2 hours to reach its destination. The percentage error of this time calculation would be expressed as follows:
Ea = 1-2
Ea = -0.2
Ep = (-0.2 / 1.2) x 100
Ep = -16%
6 - Length measurement
Any length is measured by a value of 30 cm. When verifying the measurement of this length it is evident that there was an error of 0.2 cm. The percentage error in this case would be manifested as follows:
Ep = (0.2 / 30) x 100
Ep = 0.67%
7 - Length of a Bridge
The calculation of the length of a bridge according to its planes is of 100 m. However, when confirming this length once it is built it is evident that it is actually 99.8 m long. The percentage error would be evidenced in this way.
Ea = 100 - 99.8
Ea = 0.2 m
Ep = (0.2 / 99.8) x 100
Ep = 0.2%
8 - The diameter of a screw
The head of a screw made of standard form is given to have 1 cm of diameter.
However, when measuring this diameter, it is observed that the screw head actually has 0.85 cm. The percent error would be as follows:
Ea = 1 - 0.85
Ea = 0.15 cm
Ep = (0.15 / 0.85) x 100
Ep = 17.64%
9 - Weight of an Object
According to its volume and materials, it is estimated that the weight of a given object is 30 kilos. Once the object is analyzed, it is observed that its actual weight is 32 kilos.
In this case, the percentage error value is described as follows:
Ea = 30 - 32
Ea = -2 kilos
Ep = (2/32) x 100
Ep = 6.25%
10 - Measuring Steel
In a laboratory a steel sheet is studied. When measuring the dimensions of the sheet and calculating its mass and volume, the density of the sheet (3.51 g / cm3) is determined.
However, when checking the numerical table of the material, this indicates that the density of the steel is 2.85 g / cm3. In this way, the absolute and percentage error would be calculated as follows:
Ea = 3.51-2.85
Ea = 0.66 g / cm 3.
Ep = (0.66 / 2.85) x 100%
Ep = 23.15%
References
- Fun, M. i. (2014). Math is Fun . Obtained from Percentage Error: mathsisfun.com
- Helmenstine, A.M. (February 8, 2017). ThoughtCo . Obtained from How To Calculate Percent Error: thoughtco.com
- Hurtado, A. N., & Sanchez, F.C. (s.f.). Tuxtla Gutierrez Institute of Technology . Retrieved from 1.2 Error types: Absolute error, relative error, percentage error, rounding errors, and truncation.: sites.google.com
- Iowa, U. (2017). Imaging the Universe . Obtained from Percent Error Formula: astro.physics.uiowa.edu
- Lefers, M. (July 26, 2004). Percent Error . Retrieved from Definition: groups.molbiosci.northwestern.edu.