Prefix multipliers

The SI system employs prefix multipUeis (Table 2.2) with the standard imits. These multipliers Aange the value of the imit by powers of 10. For example, the kilometer (km) has the prefix kilo-, meaning 1000 or 10. Therefore  

A The diameter of a quarter is about 2.4 cm. Question Why would you not use meters to make this measurement  

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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. 

The prefix multipliers are given in Table 1.2. It is crucial that you learn all the multipliers, as well as their numerical meanings and abbreviations. Notice some abbreviations are capital letters, while others are lower case letters. It is important that you not confuse these. The letter m is particularly overused as an abbreviation. Notice that the abbreviation for micro is the Greek letter mu (p), which is equivalent to the English letter m. 

Recall the numerical meaning of centi is 1 x 10 2, so we can substitute the prefix multiplier c for its numerical equivalent. We don t have to do this substitution to both sides because in trading c for its numerical equivalent, we haven t changed the value on the right side. 

Notice that our conversion factor between metric quantities has an interesting form. One side gets the prefix multiplier letter (in this case, the c ), and the other side gets the numerical equivalent of the multiplier (in this case, 1 x 10-2). Students sometimes get the number on the wrong side of the conversion factor. If you stick with the definition of the prefix multipliers given in Table 1.2, your conversion factors will always have a prefix multiplier on one side and a number on the other side. Seems fairer that way, doesn t it ... 

You might have learned this form in a previous class. Of course, either form of our conversion factor can be used. However, if you have ever had trouble converting between metric units, you might want to stick with the first version. Learn the prefix multipliers and their numerical meanings. Then, when you write a conversion factor expression, make sure one side gets the letter and the other side gets the number. 

Complete the following table of the metric prefix multipliers. 

Indicate how many of each element is present with a prefix multiplier (mono = 1 di = 2 tri = 3 tetra = 4 penta = 5 hexa = 6 hepta = 7 octa = 8)... 

Ionic Compounds To name an ionic compound, you just name the cation and then the anion. There is a crucial difference between naming ionic compounds and molecular compounds. In molecular compounds you must include prefix multipliers (di, tri, etc.) to indicate the number of each kind of atom in the molecule. In ionic compounds you must not include prefix multipliers, because the number of each ion in the formula unit is controlled by the charges on the ions. If the cation is a representative element, it is not necessary to indicate the charge, because (with few exceptions) these metals form cations with an ionic charge equal to the group number. 

If the compound contains more than one hydroxyl group, you need to include a prefix multiplier to indicate the number of hydroxyl groups. Two examples are shown in Figure 11.21. 

The kilogram is the standard SI base unit for mass, even though it includes a multiplier prefix. However, for the application of other prefix multipliers the base word is the gram thus 1000 kilograms is 1 Mg, not 1 kkg. 

Multiple Prefix Multiplying Prefixes Symbol Multiple Prefix Symbol... 

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. 

Table 2-2 summarizes the most commonly used prefix multipliers along with the symbols used to denote them. 

Scientific notation (see Appendix lA) allows us to express very large or very small quantities in a compact manner by using exponents. For example, the diameter of a hydrogen atom can be written as 1.06 x 10 m. The International System of Units uses the prefix multipliers shown in Table 1.2 with the standard units. These multipliers change the value of the unit by powers of 10 (just like an exponent does in scientific notation). For example, the kilometer has the prefix kilo meaning 1000 or 10. Therefore,... 

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 ... 

In Section 1.6, we learned the SI unit system, the prefix multipliers, and a few other units. Knowing how to work with and manipulate these units in calculations is central to solving chemical problems. In calculations, units help to determine correctness. Using units as a guide to solving problems is called dimensional analysis. Units should always be included in calculations they are multiplied, divided, and canceled like any other algebraic quantity. 

What are prefix multipliers List some examples. 

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

Use scientific notation to express each quantity with only the base units (no prefix multipliers). 

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