2-1 lists the primary units of measurement in the MKS system, along with their abbreviations.
Table 2-1 MKS Units of Measurement
These are the measuring sticks that will become familiar to you as you solve problems and triumph over the math in this book. Also for reference, Table 2-2 shows the primary units of measurement (and their abbreviations) in the CGS system. (Don’t bother memorizing the ones you’re not familiar with now; you can come back to them later as needed.)
Table 2-2 CGS Units of Measurement
Warning: Because different measurement systems use different standard lengths, you can get several different numbers for one part of a problem, depending on the measurement you use. For example, if you’re measuring the depth of the water in a swimming pool, you can use the MKS measurement system, which gives you an answer in meters, or the less common FPS system, in which case you determine the depth of the water in feet. The point? When working with equations, stick with the same measurement system all the way through the problem. If you don’t, your answer will be a meaningless hodgepodge, because you’re switching measuring sticks for multiple items as you try to arrive at a single answer. Mixing up the measurements causes problems – imagine baking a cake where the recipe calls for 2 cups of flour, but you use 2 liters instead.
Examples
Q. You’re told to measure the length of a racecar track using the MKS system. What unit(s) will your measurement be in?
A. The correct answer is meters. The unit of length in the MKS system is the meter.
Q. You’re told to measure the mass of a marble using the CGS system. What unit(s) will your measurement be in?
A. The correct answer is grams. The unit of mass in the CGS system is the gram.
Practice Questions
1. You’re asked to measure the time it takes the moon to circle Earth using the MKS system. What will your measurement’s units be?
2. You need to measure the force a tire exerts on the road as it’s moving using the MKS system. What are the units of your answer?
3. You’re asked to measure the amount of energy released by a firecracker when it explodes using the CGS system. What are the units of your answer?
Practice Answers
1. seconds. The unit of time in the MKS system is the second.
2. newtons. The unit of force in the MKS system is the newton.
3. ergs. The unit of energy in the CGS system is the erg.
Eliminating Some Zeros: Using Scientific Notation
Physicists have a way of getting their minds into the darndest places, and those places often involve really big or really small numbers. Physics has a way of dealing with very large and very small numbers; to help reduce clutter and make them easier to digest, it uses scientific notation.
Remember: In scientific notation, you write a number as a decimal (with only one digit before the decimal point) multiplied by a power of ten. The power of ten (10 with an exponent) expresses the number of zeroes. To get the right power of ten for a vary large number, count all the places in front of the decimal point, from right to left, up to the place just to the right of the first digit (you don’t include the first digit because you leave it in front of the decimal point in the result).
For example, say you’re dealing with the average distance between the sun and Pluto, which is about 5,890,000,000,000 meters. You have a lot of meters on your hands, accompanied by a lot of zeroes. You can write the distance between the sun and Pluto as follows:
The exponent is 12 because you count 12 places between the end of 5,890,000,000,000 (where a decimal would appear in the whole number) and the decimal’s new place after the 5.
Scientific notation also works for very small numbers, such as the one that follows, where the power of ten is negative. You count the number of places, moving left to right, from the decimal point to just after the first nonzero digit (again leaving the result with just one digit in front of the decimal):
Remember: If the number you’re working with is larger than ten, you have a positive exponent in scientific notation; if it’s smaller than one, you have a negative exponent. As you can see, handling super large or super small numbers with scientific notation is easier than writing them all out, which is why calculators come with this kind of functionality already built in.
Scientists have come up with a handy notation that helps take care of variables that have very large or very small values in their standard units. Say you’re measuring the thickness of a human hair and find it to be 0.00002 meters thick. You could use scientific notation to write this as
A more familiar unit prefix is k, as in kilo, which represents 103 times the unit. For example the kilometer, km, is 103 meters, which equals 1,000 meters. The following table shows other common unit prefixes that you may see.
Examples
Q. How does the number 1,000 look in scientific notation?
A. The correct answer is 1.0 × 103. You have to move the decimal point three times to the left to get 1.0.
Q. What is 0.000037 in scientific notation?
A. The correct answer is 3.7 × 10– 5. You have to move the decimal point five times to the right to get 3.7.
Practice Questions
1. What is 0.0043 in scientific notation?
2. What is 430,000 in scientific notation?
3. What is 0.00000056 in scientific notation?
4. What is 6,700 in scientific notation?
Practice Answers
1. 4.3 × 10– 3. You have to move the decimal
