Every measurement provides three kinds of information: the size or magnitude of the measurement (a number), a standard of comparison for the measurement (a unit), and an indication of the uncertainty of the measurement. While the number and unit are explicitly represented when a quantity is written, the uncertainty is an aspect of the errors in the measurement results.

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

The International System of Units or SI system, by international agreement, has fixed measurement units for seven fundamental properties: length, mass, time, temperature, electric current, amount of substance, and luminosity. These are called the SI base units.

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.

A physical quantity is defined either by specifying its measurement method or by stating how it is calculated from other measurements. For example, consider a metallic cube. We might define its mass and dimensions by specifying methods for measuring them, such as using a weighing machine and a meter scale. Then, we could define the volume by stating that it is the cube of its side, and we could calculate the density as the mass divided by the volume.
Measurements of physical quantities are...