Measurement Errors

Digital scale

Addition and Subtraction Measurement Errors

baythen

bayif

Δy = the absolute error in y

Δa = the absolute error in a

Δb = the absolute error in b

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1.07.8

1.02.5

ba

cmcmb

cmcmaExample:

cmcmba 2.09.137.82.5

Multiplication and Division Measurement Errors

c

c

b

b

a

a

y

ythen

c

abyif

cin error relative

bin error relative

ain error relative

yin error relative

c

cb

ba

a

y

y

??

05.024.4

1.07.8

1.02.5

c

ab

ggc

cmcmb

cmcmaExample:

Practice Problem: Calculate the surface area of the following rectangular prism.

8.4cm ±.1cm

4.5cm ±.1cm

3.2cm ±.1cm

Order of Magnitude – The power of ten closest to a given number.

Range of Magnitudes of the Universe

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

Examples:

7.0

2.0

10000

3.16

9.11 x 10-31

365

4.24 x 10-13

4,200,000

Estimate the number of heartbeats in an average human lifetime.

Estimate the volume of our body in cm3.

The mass of your backpack that contains your school materials in grams.

Fundamental of the International System (IS):

Quantity SI Unit SI Symbol

length meter m

mass kilogram kg

time second s

Electric current Ampere A

temperature Kelvin K

Matter mole mol

Luminous intensity candela cd

Random and Systematic Errors

Systematic errors push the results in the same direction. They are a system or instrument error.

Examples:A scale that has not been zeroed.A clock that runs slow or fast.Parallax error

Systematic errors present graphically as an unexpected vertical intercept or a slope which is significant different from the expected value.

Random errors are scattered about the accepted values due to variations in the performance of the instrument and operator .

Examples:Reading errorsTemperature variationsTiming errors

Random errors present graphically as scattering of data about the expected graph.

Precision and accuracy