Basic Math and Pre-Algebra For Dummies (71 page)

This method works even when one or both of the exponents are negative numbers. For example, if you follow the preceding series of steps, you find that (6.02 × 10
²³
)(9 × 10
^–28
) = 5.418 × 10
^–4
.
Note:
In decimal form, this number equals 0.0005418.

Chapter 15

In This Chapter

Using units for non-discrete measurement

Discovering differences between the English and metric systems

Estimating and calculating English and metric system conversions

In Chapter
4
, I introduce you to
units,
which are items that can be counted, such as apples, coins, or hats. Apples, coins, and hats are easy to count because they're
discrete
— that is, you can easily see where one ends and the next one begins. But not everything is so easy. For example, how do you count water — by the drop? Even if you tried, exactly how big is a drop?

Units of measurement come in handy at this point. A
unit of measurement
allows you to count something that isn't discrete: an amount of a liquid or solid, the distance from one place to another, a length of time, the speed at which you're traveling, or the temperature of the air.

In this chapter, I discuss two important systems of measurement: English and metric. You're probably familiar with the English system already, and you may know more than you think about the metric system. Each of these measurement systems provides a different way to measure distance, volume, weight (or mass), time, and speed. Next, I show you how to estimate metric amounts in English units. Finally, I show how to convert from English units to metric and vice versa.

The two most common measurement systems today are the
English system
and the
metric system
.

Most Americans learn the units of the English system — for example, pounds and ounces, feet and inches, and so forth — and use them every day. Unfortunately, the English system is awkward for use with math. English units such as inches and fluid ounces are often measured in fractions, which (as you may know from Chapters
9
and
10
) can be difficult to work with.

The
metric system
was invented to simplify the application of math to measurement. Metric units are based on the number 10, which makes them much easier to work with. Parts of units are expressed as decimals, which (as Chapter
11
shows you) are much friendlier than fractions.

Yet despite these advantages, the metric system has been slow to catch on in the U.S. Many Americans feel comfortable with English units and are reluctant to part with them. For example, if I ask you to carry a 20-lb. bag for one-fourth of a mile, you know what to expect. However, if I ask you to carry a bag weighing 10 kilograms half a kilometer, you may not be sure.

In this section, I show you the basic units of measurement for both the English and metric systems.

If you want an example
of the importance of converting carefully, you may want to look to NASA — they kind of lost a Mars orbiter in the late 1990s because an engineering team used English units and NASA used metric to navigate!

The
English system of measurement
is most commonly used in the United States (but, ironically, not in England). Although you're probably familiar with most of the English units of measurement, in the following list, I make sure you know the most important ones. I also show you some equivalent values that can help you do conversions from one type of unit to another.

• Units of distance:
  Distance — also called
  length
  — is measured in inches (in.), feet (ft.), yards (yd.), and miles (mi.):
  

  

• Units of fluid volume:
  Fluid volume (also called
  capacity
  ) is the amount of space occupied by a liquid, such as water, milk, or wine. I discuss volume when I talk about geometry in Chapter
  16
  . Volume is measured
  in fluid ounces (fl. oz.), cups (c.), pints (pt.), quarts (qt.), and gallons (gal.):
  

  

   Units of fluid volume are typically used for measuring the volume of things that can be poured. The volume of solid objects is more commonly measured in cubic units of distance, such as cubic inches and cubic feet.
  

• Units of weight:
  Weight is the measurement of how strongly gravity pulls an object toward Earth. Weight is measured in ounces (oz.), pounds (lb.), and tons.
  

  

   Don't confuse
  fluid ounces,
  which measure volume, with
  ounces,
  which measure weight. These units are two completely different types of measurements!
  

• Units of time:
  Time is hard to define, but everybody knows what it is. Time is measured in seconds, minutes, hours, days, weeks, and years:
  

  

   The conversion from days to years is approximate because Earth's daily rotation on its axis and its yearly revolution around the sun aren't exactly synchronized. A year is closer to 365.25 days, which is why leap-years exist.
  

  I left months out of the picture because the definition of a month is imprecise — it can vary from 28 to 31 days.
  

• Unit of speed:
  Speed is the measurement of how much time an object takes to move a given distance. The most common unit of speed is miles per hour (mph).
  
• Unit of temperature:
  Temperature measures how much heat an object contains. This object can be a glass of water, a turkey in the oven, or the air surrounding your house. Temperature is measured in degrees Fahrenheit (°F).