Measurement is one of the foundations of science. Scientists use measurements as part of the observation and experimental parts of the scientific method. When sharing measurements, a standard is needed to help other scientists reproduce the results of an experiment. This study guide outlines the concepts needed to work with measurements.
Accuracy
Accuracy refers to how close a measurement agrees with a known value of that measurement. If measurements were compared to shots at a target, the measurements would be the holes and the bullseye, the known value. This illustration shows holes fairly close to the center of the target but scattered widely. This set of measurements would be considered accurate.
Precision
Accuracy is important in a measurement, but it is not all that is needed. Precision refers to how well the measurements compare to each other. In this illustration, the holes are clustered closely together. This set of measurements is considered to have high precision.
Note that none of the holes are near the center of the target. Precision alone is not enough to make good measurements. It is also important to be accurate. Accuracy and precision work best when they work together.
Significant Figures and Uncertainty
When a measurement is taken, the measuring device and the skill of the individual taking the measurements play a major role in the results. If you try to measure the volume of a swimming pool with a bucket, your measurement is not going to be very accurate or precise. Significant figures are one way to show the amount of uncertainty in a measurement. The more significant figures in a measurement, the more precise the measurement. There are six rules concerning significant figures.
- All digits between two non-zero digits are significant.
321 = 3 significant figures
6.604 = 4 significant figures
10305.07 = 7 significant figures - Zeros at the end of a number and to the right of the decimal point are significant.
100 = 3 significant figures
88,000 = 5 significant figures - Zeros to the left of the first nonzero digit are NOT significant
0.001 = 1 significant figure
0.00020300 = 5 significant figures - Zeros at the end of a number greater than 1 are NOT significant unless the decimal point is present.
2,400 = 2 significant figures
2,400. = 4 significant figures - When adding or subtracting two numbers, the answer should have the same number of decimal places as the least accurate of the two numbers.
33 + 10.1 = 43, not 43.1
10.02 - 6.3 = 3.7, not 3.72 - When multiplying or dividing two numbers, the answer is rounded to have the same number of significant figures as the number with the least number of significant figures.
0.352 x 0.90876 = 0.320
7 ÷ 0.567 = 10
More Information on Significant Figures
Scientific Notation
Many calculations involve very large or very small numbers. These numbers are often expressed in a shorter, exponential form called scientific notation.
For very large numbers, the decimal is moved to the left until only one digit remains to the left of the decimal. The number of times the decimal is moved is written as an exponent to the number 10.
1,234,000 = 1.234 x 10^{6}
The decimal point was moved six times to the left, so the exponent is equal to six.
For very small numbers, the decimal is moved to the right until only one digit remains to the left of the decimal. The number of times the decimal is moved is written as a negative exponent to the number 10.
0.00000123 = 1.23 x 10^{-6}
SI Units - Standard Scientific Measurement Units
The International System of Units or "SI Units" is a standard set of units agreed on by the scientific community. This system of measurements is also commonly called the metric system, but SI units are actually based on the older metric system. The names of the units are the same as the metric system, but the SI units are based on different standards.
There are seven base units that form the foundation of the SI standards.
- Length - meter (m)
- Mass - kilogram (kg)
- Time - second (s)
- Temperature - Kelvin (K)
- Electric current - ampere (A)
- Amount of a substance - mole (mol)
- Luminous intensity - candela (cd)
Other units are all derived from these seven base units. Many of these units have their own special names, such as the unit of energy: joule. 1 joule = 1 kg·m^{2}/s^{2}. These units are called derived units.
More About Metric Units
Metric Unit Prefixes
SI units can be expressed by powers of 10 using metric prefixes. These prefixes are commonly used instead of writing very large or very small numbers of base units.
For example, instead of writing 1.24 x 10^{-9} meters, the prefix nano- can replace the 10^{-9} exponent or 1.24 nanometers.