2.1 Measurements
Learning Objectives
By the end of this section, you will be able to:
- Understand and apply fundamental measurements in scientific notation.
- Employ Systeme Internationale (SI) measurements
Scientific Notation
Scientific Notation is a method to simplify very large and very small numbers by utilizing a base 10 exponential methodology. The in above examples given 298 000 kg is equivalent to 2.98 ×
10 ×
10 ×
10 ×
10 ×
10 ×
10 or 2.98×105 whereas, 0.0000025 kilograms, is equivalent to 2.5 ×
1/10 ×
1/10 ×
1/10 ×
1/10 ×
1/10 ×
1/10 or 2.5 x 10−6 kg. Using a scientific calculator effectively can reduce the introduction of calculation errors. For example, 298 000 can be inputted as 2.98 [EXP] 5 as scientific notation of the former example.
Units
Units, such as litres, pounds, and centimetres, are standards of comparison for measurements. When we buy a 2-litre bottle of a soft drink, we expect that the volume of the drink was measured, so it is two times larger than the volume that everyone agrees to be 1 litre. The meat used to prepare a 0.25-pound hamburger is measured so it weighs one-fourth as much as 1 pound. Without units, a number can be meaningless, confusing, or possibly life threatening. Suppose a doctor prescribes phenobarbital to control a patient’s seizures and states a dosage of “100” without specifying units. Not only will this be confusing to the medical professional giving the dose, but the consequences can be dire: 100 mg given three times per day can be effective as an anticonvulsant, but a single dose of 100 g is more than 10 times the lethal amount.
We usually report the results of scientific measurements in SI units, an updated version of the metric system, using the units listed in Table 2.1a. Other units can be derived from these base units. The standards for these units are fixed by international agreement, and they are called the International System of Units or SI Units (from the French, Le Système International d’Unités). SI units have been used by the United States National Institute of Standards and Technology (NIST) since 1964.
| Property Measured | Name of Unit | Symbol of Unit |
|---|---|---|
| length | meter | m |
| mass | kilogram | kg |
| time | second | s |
| temperature | kelvin | K |
| electric current | ampere | A |
| amount of substance | mole | mol |
| luminous intensity | candela | cd |
Sometimes we use units that are fractions or multiples of a base unit. Ice cream is sold in quarts (a familiar, non-SI base unit), pints (0.5 quart), or gallons (4 quarts). We also use fractions or multiples of units in the SI system, but these fractions or multiples are always powers of 10. Fractional or multiple SI units are named using a prefix and the name of the base unit. For example, a length of 1000 meters is also called a kilometre because the prefix kilo means “one thousand,” which in scientific notation is 103 (1 kilometre = 1000 m = 103 m). The prefixes used and the powers to which 10 are raised are l