ccna1 v3 module 2 w04 – sault college – bazlurslide 1 accuracy vs. precision

CCNA1 v3 Module 2 W04 – Sault College – Bazlur slide 1

Accuracy vs. Precision

PHY115 – Sault College – Bazlur slide 2

Physics• It comes from the Latin word “physica”, meaning

nature.• Physics is the study of laws of nature that govern the

physical world around us.• Physics is the branch of science that deals with the

properties, changes, and interactions of matter and energy.


Physics• Physics is an important science: • it increases our understanding of numerous

phenomena; • It is the foundation for further studies in science,

engineering, and technology;• and it is the stepping stone to many careers.


Measurement• Measurement is a process of comparing an unknown

value to a known value.• A measurement may be expressed in terms of its

accuracy or its precision.


Accuracy vs. Precision• Accuracy: A measure of how close an

experimental result is to the true value.

• Precision: A measure of how exactly the result is determined. It is also a measure of how reproducible the result is.

– Absolute precision: indicates the uncertainty in the same units as the observation

– Relative precision: indicates the uncertainty in terms of a fraction of the value of the result


Accuracy• Physicists are interested in how closely a

measurement agrees with the true value.• This is an indication of the quality of the measuring

instrument.• Accuracy is a means of describing how closely a

measurement agrees with the actual size of a quantity being measured.


Error• The difference between an observed value and the

true value is called the error.• The size of the error is an indication of the accuracy.• Thus, the smaller the error, the greater the accuracy.

• The percentage error determined by subtracting the true value from the measured value, dividing this by the true value, and multiplying by 100.

%100x

valuetrue

valuetruevaluemeasured error percentage


Error

%100x

valuetrue

valuetruevaluemeasured error percentage

%4

%100x5.2

1.0

%100x5.2

5.26.2

m

mm

mm error percentage


Significant Digits• The accuracy of a measurement is indicated by the

number of significant digits.• Significant digits are those digits in the numerical

value of which we are reasonably sure.• More significant digits in a measurement the accurate

it is:


Significant Digits• More significant digits in a measurement the accurate

it is:

E.g., the true value of a bar is 2.50 m

Measured value is 2.6 m with 3 significant digits.

The percentage error is (2.6-2.50)*100/2.50 = 4%



The percentage error is (2.55-2.50)*100/2.50 = 0.2%

Which one is more accurate? The one which has more significant digits


Precision• Being precise means being sharply defined.• The precision of a measuring instrument depends on

its degree of fineness and the size of the unit being used.

• Using an instrument with a more finely divided scale allows us to take a more precise measurement.


Precision• The precision of a measuring refers to the smallest

unit with which a measurement is made, that is, the position of the last significant digit.

• In most cases it is the number of decimal places.

• E.g.,• The precision of the measurement 385,000 km

is 1000 km. (the position of the last significant digit is in the thousands place.)

• The precision of the measurement 0.025m is 0.001m. (the position of the last significant digit is in the thousandths place.)


How precise do we need?• Physicists are interested in how closely a

measurement agrees with the true value.• That is, to achieve a smaller error or more accuracy.

• For bigger quantities, we do not need to be precise to be accurate.


How precise do we need?• For bigger quantities, we do not need to be precise to be

accurate.

E.g., the true value of a bar is 25 m

Measured value is 26 m with 2 significant digits.

The percentage error is (26-25)*100/25 = 4%



The percentage error is (2.6-2.5)*100/2.5 = 4%

Which one is more precise? The one which has the precision of 0.1m

Which one is more accurate? Both are same accurate as both have 2 significant digits


Accuracy or Relative Precision• An accurate measurement is also known as a

relatively precise measurement.

• Accuracy or Relative Precision refers to the number of significant digits in a measurement.

• A measurement with higher number of significant digits closely agrees with the true value.


Estimate• Any measurement that falls between the smallest

divisions on the measuring instrument is an estimate.• We should always try to read any instrument by

estimating tenths of the smallest division.


Accuracy or Relative Precision• In any measurement, the number of significant figures are

critical. • The number of significant figures is the number of digits

believed to be correct by the person doing the measuring. • It includes one estimated digit. • A rule of thumb: read a measurement to 1/10 or 0.1 of the

smallest division. • This means that the error in reading (called the reading error) is

1/10 or 0.1 of the smallest division on the ruler or other instrument.

• If you are less sure of yourself, you can read to 1/5 or 0.2 of the smallest division.

• http://www.astro.washington.edu/labs/clearinghouse/labs/Scimeth/mr-sigfg.html


Exact vs. Approximate numbers• An exact number is a number that has been

determined as a result of counting or by some definition.

41 students are enrolled in this class

1 in = 2.54 cm

• Nearly all data of a technical nature involve approximate numbers.

• That is numbers determined as a result of some measurement process, as with a ruler.

• No measurement can be found exactly.


Calculations with Measurements• The sum or difference of measurements can be no

more precise than the least precise measurement.• Round the results to the same precision as the least

precise measurement.

42.28 mmUsing a micrometer

54 mmUsing a ruler,

Precision of the ruler is 1 mmBut actually it can be anywhere

between 53.50 to 54.50 mm

This means that the tenths and hundredths digits in the sum 96.28 mm are really meaningless,

the sum should be 96 mm with a precision of 1 mm


Calculations with Measurements• The product or quotient of measurements can be no

more accurate than the least accurate measurement.• Round the results to the same number of significant

digits as the measurement with the least number of significant digits.

• http://www.astro.washington.edu/labs/clearinghouse/labs/Scimeth/mr-sigfg.html

Length of a rectangle is 54.7 mWidth of a rectangle is 21.5 mArea is 1176.05 m2

Area should be rounded to 1180 m2

To express with same accuracy


Examples of Rounding• http://www.astro.washington.edu/labs/clearingh

ouse/labs/Scimeth/mr-sigfg.html

ccna1 v3 module 2 w04 – sault college – bazlurslide 1 accuracy vs. precision

Documents