Express the answer to this calculation using the appropriate number of significant figures:
3. Report the difference using the appropriate number of significant figures:
4. Express the answer to this multi-step calculation using the appropriate number of significant figures:
Practice Answers
1. 114.36 seconds. The trick here is remembering to convert all measurements to the same power of 10 before comparing decimal places for significant figures. Doing so reveals that
2.
The raw calculation yields 4,147.2 inches, which rounds properly to four significant figures as 4,147 inches, or
3. –0.009 minutes. Here, it helps here to convert all measurements to the same power of 10 so you can more easily compare decimal places in order to assign the proper number of significant figures. Doing so reveals that
4. 2.80 feet. Following standard order of operations, you can do this problem in two main steps.
Following the rules of significant-figure math, the first step yields
After completing the first step, divide by 10.0 feet to finish the problem:
You write the answer with three sig figs because the measurement 10.0 feet contains three sig figs, which is the smallest available between the two numbers.
Chapter 2
Using and Converting Units
In This Chapter
▶ The SI system, base units, and prefixes
▶ Creating derived units and examining density
▶ How to use conversion factors
▶ Solving with the factor label method
Have you ever been asked for your height in centimeters, your weight in kilograms, or the speed limit in kilometers per hour? These measurements may seem a bit odd to those folks who are used to feet, pounds, and miles per hour, but the truth is that scientists sneer at feet, pounds, and miles. Because scientists around the globe constantly communicate numbers to each other, they prefer a highly systematic, standardized system. The International System of Units, abbreviated SI from the French term Système International, is the unit system of choice in the scientific community.
In this chapter, you find that the SI system offers a very logical and well-organized set of units. Scientists, despite what many of their hairstyles may imply, love logic and order, so SI is their system of choice.
Tip: As you work with SI units, try to develop a good sense for how big or small the various units are. That way, as you’re doing problems, you’ll have a sense for whether your answer is reasonable.
Familiarizing Yourself with Base Units and Metric System Prefixes
Much of the work chemists do involves measuring physical properties, such as the mass, volume, or length of a substance. Because chemists must be able to communicate their measurements to other chemists all over the world, they need to speak the same measurement language. This language is the SI system of measurement, related to the metric system, which you’ve hopefully used before. Minor differences exist between the SI and metric systems, but for the most part, they’re very similar.
To correctly use the SI system, you need to have a firm understanding of what each prefix means. The good news: The SI system is a decimal system. In other words, it’s easy to use as long as you know the prefixes.
SI has base units for mass, length, volume, and so on, and prefixes modify the base units. For example, kilo– means 1,000; a kilogram is 1,000 grams, and a kilometer is 1,000 meters. Use Table 2-1 as a handy reference for the abbreviations and meanings of some selected various SI prefixes.
Table 2-1 SI (Metric) Prefixes
The next step in mastering the SI system is to figure out all the possible units that you can run into when solving problems. Here’s a quick explanation of the most common types of units you’ll encounter.
Units of length
The base unit for length in the SI system is the meter. The exact definition of meter has changed over the years, but it’s now defined as the distance that light travels in a vacuum in
1 millimeter (mm) = 1,000 micrometers (µm)
1 centimeter (cm) = 10 millimeters (mm)
1 meter (m) = 100 centimeters (cm)
1 kilometer (km) = 1,000 meters (m)
Some common English-to-SI-system length conversions are
1 mile (mi) = 1.61 kilometers (km)
1 yard (yd) = 0.914 meters (m)
1 inch (in.) = 2.54 centimeters (cm)
Units of mass
The base unit for mass in the SI system is the kilogram. It’s the weight of the standard platinum-iridium bar found at the International Bureau of Weights and Measures. Here are some SI units
