<< Chapter < Page Chapter >> Page >

Percent uncertainty

One method of expressing uncertainty is as a percent of the measured value. If a measurement A size 12{A} {} is expressed with uncertainty, δA size 12{δA} {} , the percent uncertainty    (%unc) is defined to be

% unc = δA A × 100% . size 12{%" unc = " { {δA} over {A} } times "100"%} {}

Calculating percent uncertainty: a bag of apples

A grocery store sells 5-lb size 12{ "5-lb" } {} bags of apples. You purchase four bags over the course of a month and weigh the apples each time. You obtain the following measurements:

  • Week 1 weight: 4.8 lb size 12{ "4.8 lb" } {}
  • Week 2 weight: 5.3 lb size 12{ "5.3 lb" } {}
  • Week 3 weight: 4.9 lb size 12{ "4.9 lb" } {}
  • Week 4 weight: 5.4 lb size 12{ "5.4 lb" } {}

You determine that the weight of the 5-lb size 12{ "5-lb" } {} bag has an uncertainty of ± 0 . 4 lb size 12{ +- 0 "." 4`"lb"} {} . What is the percent uncertainty of the bag’s weight?

Strategy

First, observe that the expected value of the bag’s weight, A size 12{A} {} , is 5 lb. The uncertainty in this value, δA size 12{δA} {} , is 0.4 lb. We can use the following equation to determine the percent uncertainty of the weight:

% unc = δA A × 100% . size 12{%" unc = " { {δA} over {A} } times "100"%} {}

Solution

Plug the known values into the equation:

% unc = 0 . 4  lb 5  lb × 100% = 8 % . size 12{%" unc = " { {0 "." 4" lb"} over {5" lb"} } times "100"%=8%} {}

Discussion

We can conclude that the weight of the apple bag is 5 lb ± 8 % size 12{5`"lb" +- 8%} {} . Consider how this percent uncertainty would change if the bag of apples were half as heavy, but the uncertainty in the weight remained the same. Hint for future calculations: when calculating percent uncertainty, always remember that you must multiply the fraction by 100%. If you do not do this, you will have a decimal quantity, not a percent value.

Got questions? Get instant answers now!

Uncertainties in calculations

There is an uncertainty in anything calculated from measured quantities. For example, the area of a floor calculated from measurements of its length and width has an uncertainty because the length and width have uncertainties. How big is the uncertainty in something you calculate by multiplication or division? If the measurements going into the calculation have small uncertainties (a few percent or less), then the method of adding percents    can be used for multiplication or division. This method says that the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation . For example, if a floor has a length of 4 . 00 m size 12{4 "." "00"" m"} {} and a width of 3 . 00 m size 12{3 "." "00"" m"} {} , with uncertainties of 2% size 12{2%} {} and 1% size 12{1%} {} , respectively, then the area of the floor is 12 . 0 m 2 size 12{"12" "." 0" m" rSup { size 8{2} } } {} and has an uncertainty of 3% size 12{3%} {} . (Expressed as an area this is 0 . 36 m 2 size 12{0 "." "36"" m" rSup { size 8{2} } } {} , which we round to 0 . 4 m 2 size 12{0 "." 4" m" rSup { size 8{2} } } {} since the area of the floor is given to a tenth of a square meter.)

A high school track coach has just purchased a new stopwatch. The stopwatch manual states that the stopwatch has an uncertainty of ± 0 . 05 s size 12{ +- 0 "." "05"`s} {} . Runners on the track coach’s team regularly clock 100-m sprints of 11.49 s size 12{"11.49 s"} {} to 15.01 s size 12{"15.01 s"} {} . At the school’s last track meet, the first-place sprinter came in at 12 . 04 s size 12{"12" "." "04"" s"} {} and the second-place sprinter came in at 12 . 07 s size 12{"12" "." "07"" s"} {} . Will the coach’s new stopwatch be helpful in timing the sprint team? Why or why not?

No, the uncertainty in the stopwatch is too great to effectively differentiate between the sprint times.

Got questions? Get instant answers now!

Precision of measuring tools and significant figures

An important factor in the accuracy and precision of measurements involves the precision of the measuring tool. In general, a precise measuring tool is one that can measure values in very small increments. For example, a standard ruler can measure length to the nearest millimeter, while a caliper can measure length to the nearest 0.01 millimeter. The caliper is a more precise measuring tool because it can measure extremely small differences in length. The more precise the measuring tool, the more precise and accurate the measurements can be.

Questions & Answers

where Newton second law applies
Latief Reply
A soccer player kicked off a ball at velocity of 62 ft/s at angle 45°. A goal keeper is 43 yard away from the direction in which ball kicked off. At what minimum velocity he runs to meet the ball?
Ram Reply
A soccer player kicked off the ball at the velocity of 62 ft/s at 45° with horizontal.A goal keeper is 43 yard away from the ball kicked position.At what minimum velocity he runs to meet the ball?
Ram
what is torque
Deepak Reply
The turning effect of force is called torque.
Uzair
What is the effect of static electricity
Ruth
what there factors affect the surface tension of a liquid
Promise Reply
formula for impedance
muyiwa Reply
ehat is central forces
Nita Reply
what is distance?
Jonathan Reply
What does mean ohms law imply
Victoria Reply
ohms law state that the electricity passing through a metallic conductor is directly proportional to the potential difference across its end
muyiwa
what is matter
folajin Reply
Anything that occupies space
Kevin
Any thing that has weight and occupies space
Victoria
Anything which we can feel by any of our 5 sense organs
Suraj
Right
Roben
thanks
Suraj
what is a sulphate
Alo
any answers
Alo
the time rate of increase in velocity is called
Blessing Reply
acceleration
Emma
What is uniform velocity
Victoria
Greetings,users of that wonderful app.
Frank Reply
how to solve pressure?
Cruz Reply
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?
Bern
what is coplanar force?
OLADITI Reply
forces acting and lying on d same plane
Promise
what is accuracy and precision
Peace Reply
How does a current follow?
Vineeta Reply
follow?
akif
which one dc or ac current.
akif
how does a current following?
Vineeta
?
akif
AC current
Vineeta
AC current follows due to changing electric field and magnetic field.
akif
you guys are just saying follow is flow not follow please
Abubakar
ok bro thanks
akif
flows
Abubakar
but i wanted to understand him/her in his own language
akif
but I think the statement is written in English not any other language
Abubakar
my mean that in which form he/she written this,will understand better in this form, i write.
akif
ok
Abubakar
ok thanks bro. my mistake
Vineeta
u are welcome
Abubakar
Practice Key Terms 6

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask