Precision refers to the closeness of two or more measurements to each other. Precision is a measure of the detail in which a quantity is expressed. Precision is independent of accuracy.
Precision is the quantity or state of being precise exactness. It is the degree of refinement with which an operation is performed or a measurement stated. Precision refers to the resolution or the limit to which the quantity is measured. It is determined by the least count of the measuring instrument.
Example:
(1) If you weigh a given substance five times, and get 2.7 kg each time then your measurement is very precise.
(2) If the temperature outside a building is 40^oC as measured by a weather thermometer and if the real outside temperature is 40^oC, then the thermometer is accurate. If the thermometer consistently registers this exact temperature in a row the thermometer is precise.
Accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity. A measurement system can be accurate but not precise, precise but not accurate, or neither, or both.
Example:
If an experiment containing a systematic error then increasing the sample size generally increases precision but does not improve accuracy.
If a measurement is precise, that does not necessarily mean that it is accurate. However, if the measurement is consistently accurate, it is also precise.

Illustration: Target shooting is an example which explains the difference between accuracy and precision. In Figure, the shots are focused so as to reach the bull's eye (midpoint), but the arrows have reached only around this point. Hence the shots are not accurate and also not precise.
In Figure (b), all the shots are close to each other but not at the central point. Hence the shots are said to be precise but not accurate. In Figure (c), the shots are closer and also at the central point. Hence the shots are both precise and accurate.

\(Mass\ m = 4\pm0.03\) kg ( m + \(\triangle\) m )
Volume \(V=5\pm.01 m^3(V+\triangle V)\)
Density =?
Error in mass \(={{\triangle m}\over{m}}={{0.03}\over{4}}\times 100\)
= 0.75%
Error in volume \(={{\triangle V}\over{V}}={{0.01}\over{5}}\times 100\)
= 0.2%
\(Density={{mass}\over{volume}}.\)
Error in density = error in mass + error in volume
= 0.75% +0.2% = 0.95%

Let the dimensions of Energy, Length and Time be [E],[L],[T] respectively.
We know that Force = mass x acceleration
\(Mass ={{Force}\over{acceleration}}\)
\(={{Workdone or Energy}\over{acceleration \times displacement}}\)
\([m]={{Energy}\over{[acceleration][displacement]}}\)
\(={{[E]}\over{[{LT}^{-2}][L]}}={{[E]}\over{[L^2{T}^{-2}]}}=[{EL}^{-2}{T}^{2}]\)

By the principle of homogeneity, a / V² is of the dimensions of pressure and b is of the dimensions of volume.
[a] = [pressure] [V²] = [ML⁻¹T⁻²] [L⁶]
= [ML⁵T^-2]
[b] = [V] = L³