Measurement prefix multipliers

The metric system consists of a base unit and (sometimes) a prefix multiplier. Most scientists and healthcare providers use the metric system, and you are probably familiar with the common base units and prefix multipliers. The base units describe the type of quantity measured length, mass, or time. The SI system is sometimes called the MKS (meter, kilogram, second) system, because these are the standard units of length, mass, and time upon which derived quantities, such as energy, pressure, and force, are based. An older system is called the CGS (centimeter, gram, second) system. The derived CGS units are becoming extinct. Therefore, we will focus on the MKS units. 

The prefix multipliers increase or decrease the size of the base unit, so that it more conveniently describes the system being measured. The base units that we will be using are listed in Table 1.1. For the purists, it is not strictly correct to include liters as a base unit, because volume is derived from length, and thus the official SI unit of volume is the cubic meter (m3), which is derived from the length base unit, the meter. Chemists frequently express mass in units of grams, which is derived from the kilogram. There are three other SI base units (the mole, the candela, and the ampere). We will consider moles (amount of material) and amperes (electric current) in subsequent chapters. The candela is a unit of light intensity or luminosity and does not concern us at this point. 

To simphfy presentation when your experimental data consist of either very large or very small numbers, the plotted values may be the measured numbers multiplied by a power of 10 this multiplying power should be written immediately before the descriptive label on the appropriate axis (as in Fig. 37.3). However, it is often better to modify the primary unit with an appropriate prefix (p. 70) to avoid any confusion regarding negative powers of 10. 

The prefix multipliers allow us to express a wide range of measurements in units that are similar in size to the quantity we are measuring. You should choose the prefix multiplier that is most convenient for a particular measurement. For example, to measure the diameter of a quarter, use centimeters because a quarter has a diameter of about 2.4 cm. A centimeter is a common metric unit and is about equivalent to the width of a pinky finger (2.54cm = lin.). The millimeter could also work to express the diameter of the quarter then the quarter would measure 24 mm. The kilometer, however, would not work as well since, in that unit, the quarter s diameter is 0.000024 km. Pick a unit similar in size to (or smaller than) the quantity you are measuring. Consider expressing the length of a short chemical bond, about 1.2 X 10 m. Which prefix multiplier should you use The most convenient one is probably the picometer (pico = 10 ). Chemical bonds measure about 120 pm. 

Units Measured quantities usually have units associated with them. The SI unit for length is the meter for mass, the kilogram and for time, the second. Prefix multipliers such as kilo- or milli- are often used in combination with these basic units. The SI units of volume are units of length raised to the third power liters or milliliters are often used as well. 

Suppose you are trying to measure the diameter of a Frisbee. What unit and prefix multiplier should you... 

For measuring a Frisbee, the unit would be the meter and the prefix multiplier would be centi-. The final measurement would be in centimeters. 

When reporting a measurement, choose a prefix multipher close to the size of the quantity you are measuring. For example, to state the diameter of a hydrogen atom, which is 1.06 X 10 °m, use picometers (106 pm) ornanometers (0.106 nm)ratherthan micrometers or millimeters. Choose the prefix multiplier that is most convenient for a particular number. 

What prefix multiplier is appropriate for reporting a measurement of 5.57 X 10 m ... 

Use the prefix multipliers to express each measurement without any exponents. 

One reason for the great diversity of units in existence is the fact that quantities of such diverse magnitudes are measured. A general rule is that the unit should be appropriate in magnitude to the quantity being measured. To obtain a dimension of convenient size in SI units, the SI unit is multiplied by a power of 10 and the prefixes listed in Table B.3 are affixed to the unit. 

For very large numbers with units of measure, use scientific notation or choose an appropriate multiplying prefix for the unit to avoid numbers of more than four digits. 

Express each measurement as a number separated from its units by a space. If a prefix is required, no space is left between the prefix and the unit it refers to. Symbols for units are only written in their singular form and do not require full stops to show that they are abbreviated or that they are being multiplied together. 

The metric system is a decimal-based system in contrast to the English system. In the metric system, mass is represented as the gram, length as the meter, and volume as the liter. Any subunit or multiple unit contains one of these units preceded by a prefix indicating the power of ten by which the base unit is to be multiplied to form the subunit or multiple unit. Scientists favor this system over the not-so-systematic English units of measurement. 

The following table gives conversion factors from various units of measure to SI units. It is reproduced from NIST Special Publication 811, Guide for the Use of the International System of Units (SI). The table gives the factor by which a quantity expressed in a non-SI unit should be multiplied in order to calculate its value in the SI. The SI values are expressed in terms of the base, supplementary, and derived units of SI in order to provide a coherent presentation of the conversion factors and facilitate computations (see the table International System of Units in this section). If desired, powers of ten can be avoided by using SI prefixes and shifting the decimal point if necessary. 

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