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  • Determine the appropriate number of significant figures in both addition and subtraction, as well as multiplication and division calculations.
  • Calculate the percent uncertainty of a measurement.
An old rusted double-pan balance is shown with a weighing stone on one pan.
A double-pan mechanical balance is used to compare different masses. Usually an object with unknown mass is placed in one pan and objects of known mass are placed in the other pan. When the bar that connects the two pans is horizontal, then the masses in both pans are equal. The “known masses” are typically metal cylinders of standard mass such as 1 gram, 10 grams, and 100 grams. (credit: Serge Melki)
A digital analytical balance.
Many mechanical balances, such as double-pan balances, have been replaced by digital scales, which can typically measure the mass of an object more precisely. Whereas a mechanical balance may only read the mass of an object to the nearest tenth of a gram, many digital scales can measure the mass of an object up to the nearest thousandth of a gram. (credit: Karel Jakubec)

Accuracy and precision of a measurement

Science is based on observation and experiment—that is, on measurements. Accuracy is how close a measurement is to the correct value for that measurement. For example, let us say that you are measuring the length of standard computer paper. The packaging in which you purchased the paper states that it is 11.0 inches long. You measure the length of the paper three times and obtain the following measurements: 11.1 in., 11.2 in., and 10.9 in. These measurements are quite accurate because they are very close to the correct value of 11.0 inches. In contrast, if you had obtained a measurement of 12 inches, your measurement would not be very accurate.

The precision    of a measurement system is refers to how close the agreement is between repeated measurements (which are repeated under the same conditions). Consider the example of the paper measurements. The precision of the measurements refers to the spread of the measured values. One way to analyze the precision of the measurements would be to determine the range, or difference, between the lowest and the highest measured values. In that case, the lowest value was 10.9 in. and the highest value was 11.2 in. Thus, the measured values deviated from each other by at most 0.3 in. These measurements were relatively precise because they did not vary too much in value. However, if the measured values had been 10.9, 11.1, and 11.9, then the measurements would not be very precise because there would be significant variation from one measurement to another.

The measurements in the paper example are both accurate and precise, but in some cases, measurements are accurate but not precise, or they are precise but not accurate. Let us consider an example of a GPS system that is attempting to locate the position of a restaurant in a city. Think of the restaurant location as existing at the center of a bull’s-eye target, and think of each GPS attempt to locate the restaurant as a black dot. In [link] , you can see that the GPS measurements are spread out far apart from each other, but they are all relatively close to the actual location of the restaurant at the center of the target. This indicates a low precision, high accuracy measuring system. However, in [link] , the GPS measurements are concentrated quite closely to one another, but they are far away from the target location. This indicates a high precision, low accuracy measuring system.

Questions & Answers

Suppose that a grandfather clock is running slowly; that is, the time it takes to complete each cycle is longer than it should be. Should you (@) shorten or (b) lengthen the pendulam to make the clock keep attain the preferred time?
Aj Reply
I think you shorten am not sure
Uche
shorten it, since that is practice able using the simple pendulum as experiment
Silvia
it'll always give the results needed no need to adjust the length, it is always measured by the starting time and ending time by the clock
Paul
it's not in relation to other clocks
Paul
wat is d formular for newton's third principle
Silvia
okay
Silvia
discuss under damped
Prince Reply
resistance of thermometer in relation to temperature
Ifeanyi Reply
how
Bernard
that resistance is not measured yet, it may be probably in the next generation of scientists
Paul
Is fundamental quantities under physical quantities?
Igwe Reply
please I didn't not understand the concept of the physical therapy
John Reply
physiotherapy - it's a practice of exercising for healthy living.
Paul
what chapter is this?
Anderson
this is not in this book, it's from other experiences.
Paul
please I have probably with calculate please can you please and help me out
John Reply
Sure
Gift
What is Boyce law
Sly Reply
how to convert meter per second to kilometers per hour
grace Reply
Divide with 3.6
Mateo
multiply by (km/1000m) x (3600 s/h) -> 3.6
Muhammad
2 how heat loss is prevented in a vacuum flask
Abdullah Reply
what is science
Helen
logical reasoning for a particular phenomenon.
Ajay
I don't know anything about it 😔. I'm sorry, please forgive 😔
Adarsh
due to non in contact mean no conduction and no convection bec of non conducting base and walls and also their is a grape between the layer like to take the example of thermo flask
Abdul
dimensions v²=u²+2at
Lagben Reply
what if time is not given in finding the average velocity?
Alan Reply
the magnetic circuit of a certain of the flux paths in each of the long and short sides being 25cm and 20cm reprectielectrove. there is an air gap of 2mm long in one the long sides if a flux density of 0.8weber/m is to produce in the magnet of 1500 turns..
Daniel Reply
How do you calculate precision
Sacky Reply
what module is that?
Fillemon
Chemisty 1A?
Fillemon
No it has something to do with measurements bro... What we did today in class
Sacky
Tah bra honestly I didn't understand a thing in that class..when re your Tutorials?
Fillemon
Friday bro... But the topics we did are in this app... Just try to master them quickly before the test dates... Are you done with the Maths sheet
Sacky
I eat ass
Anderson
I'll work on the maths sheet tomorrow bra @Sacky Malyenge but I'll try mastering them
Fillemon
I'll eat your mom's ass with a side of tendies
Anderson
@Fillemon Nanwaapo
Anderson
lol, hush
Emi
There are very large numbers of charged particles in most objects. Why, then, don’t most objects exhibit static electricity?
Bilkisu Reply
Because there's an equal number of negative and positive charges... objects are neutral in nature
NELSON
when a ball rolls on a smooth level ground,the motion of its centre is?
Mary Reply
what is electro magnetic field?
Mary
electromagnetic field is a special type of field been produced by electric charges..!!! like the word electro from Electricity and the word magnetic from Magnetism.. so it is more of a join field..!!!
NELSON
Electromagnetic field is caused by moving electric charge
Muhammad
when a ball rolls on a smooth level ground,the motion of its centre is?
Mumeh
Practice Key Terms 6

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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