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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Many mechanical balances, such as double-pan balances, have been replaced by digital scales, which can typically measure the mass of an object more precisely.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

Will the current used on the load side affect the current on the supply side.
Shevanan Reply
wave is a disturbance that travels through a medium and transfer energy from one place to another without causing any permanent displacement of the medium itself
Bello Reply
what is wave
atiba Reply
wave is a disturbance that travels through a medium and transfer energy from one place to another without causing any permanent displacement of the medium itself
Bello
measurements of the period of a simple pendulum in an experiment are 20 oscillations for a give length of the pendulum 30.50secs
Praise Reply
patient with a pacemaker is mistakenly being scanned for an MRI image. A 10.0-cm-long section of pacemaker wire moves at a speed of 10.0 cm/s perpendicular to the MRI unit’s magnetic field and a 20.0-mV Hall voltage is induced. What is the magnetic field strength
Muhammad Reply
fundamental and derived quantities
Kadijatu Reply
is any thing that has weight or mass and can occupy space
Kadijatu
explain why the earth is an exact shere
Akinyemi Reply
because the pull of gravity is equal on all sides
Paul
how long did sun take to rich the earth
Billy
A tennis ball is projected vertically up with a velocity of 100m/s the top of a tower 50m high. Determine the a). height reach from the ground. b). Time to reach the hmax.
Luca Reply
100×50=5000
Muhammad
what are the formula and calculation
Brianca Reply
what are the formula for resistance, ohm's law, and electric current
Brianca
I=V/R and so R=V/I
Akiiza
what is gamma rays
Uche Reply
gamma ray is an energetic ray .it does not have acharge
Merkew
what is wave
Faruq Reply
What happens to the mass of water in a pot when it cools, assuming no molecules escape or are added? Is this observable in practice? Explain.
Angel Reply
please explain to me,coz I have no idea
Brianca
what is a magnetic field
Jedaiah Reply
magnetic field is the area around a magnet where the magnetic force is exerted or felt.
Paul
what is the first Faraday's law
Abba
Formula for Newton 1st law
Maryam Reply
what is physics
Isa Reply
Physics is a way to see and solve things around us
Prajukta
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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