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What Is an Average? Suppose that your class is doing an experiment to determine the boiling point of a particular liquid. Working in groups, your classmates come up with several answers that are all slightly different. Your teacher asks you to determine which temperature best represents all of the varying results from the class. A mathematical tool called an average, or mean, will help you solve the problem. An average allows you to simplify a list of numbers into a single number that approximates the value of all of them. Check it out! PROCEDURE: To calculate the average of any set of numbers, first add all of the
numbers to find the sum. Then divide the sum by the amount of numbers in your set. The result is the average of your numbers. SAMPLE PROBLEM: Find the average of the following set of numbers:
5, 4, 7, 8 Step 1: Find the sum.
5 4 7 8 24 Step 2: Divide the sum by the amount of numbers in your set. Because there are
four numbers in your set, divide the sum by 4. 24 24 4 6 or 4 6 MATH SKILLS
The average of the numbers is 6.
Practice Your Skills! 1. Find the average of each of the following sets of numbers. a. 19 m, 11 m, 29 m, 62 m, 14 m
What Is SI? To make sharing information easier, most of the world uses the SI of measurement. SI, which stands for Système Internationale d’Unités, is a standard for measuring mass, length, volume, and other quantities. It is used by all scientists to avoid the confusion of comparing data that is based on Quantity Unit Symbol different measuring systems. Three common SI units are length meter m in the chart at right. Obviously, these three units are not volume liter L suitable for all measuring needs. But most quantities can be measured using one of these units with one of the premass gram g fixes in the chart below.
Powers of 10
meter (m), gram (g), liter (L)
0.01 (10 )
milliliter (mL) MATH SKILLS
in the chart above. If you are converting from a smaller prefix to a larger prefix (moving up the chart), divide your number by a power of 10. If you are converting from a larger prefix to a smaller prefix (moving down the chart), multiply your number by a power of 10. SAMPLE PROBLEM A: Convert 500 decimeters (dm) to kilometers (km).
▼ ▼ ▼
Step 1: Find the prefixes of the numbers.
decimeters to kilometers Step 2: Notice that you will move up the chart four places when converting
from deci- to kilo-. Therefore, you will divide your number by 10 10 10 10, or 10,000. 500 10,000 5 0 0 → 0.05 500 decimeters (dm) 0.05 kilometers (km)
SAMPLE PROBLEM B: 2.5 centiliters (cL) is how many milliliters (mL)? Step 1: Find the prefixes.
centiliters to milliliters Step 2: Because you move down the chart one place when converting from
centi- to milli-, multiply your number by 10. 2.5 10 2. 5 → 25 2.5 centiliters (cL) 25 milliliters (mL)
PROCEDURE: To convert between SI units, first find the prefixes of your numbers
MATH SKILLS FOR SCIENCE
What Is SI? continued
Work with the System! 1. Write True or False next to each statement. a. 12 hg 1.2 kg
False b. 54 cm 5.4 mm ______________
c. 0.5 dL 0.005 cL
d. 4.5 g 0.45 dag
e. 111 cm 1.11 m
False f. 7 cL 70,000 kL ______________
2. Fill in the missing numbers and units in the equations below. a. 25 mm
b. 27 kg
c. 50 cm
d. 1.2 dL
f. 41 hm 4,100,000
e. 0.9 L
3. 1 m
4. 5 kg
5. Special balances can weigh to the 0.00000001 g. How many kilograms is this? 0.00000001 g 0.00000000001 kg
6. A chemistry experiment calls for 5 g of baking soda. Your measuring spoon holds 5000 mg of powder. How many scoops will you need for the experiment?
Challenge Yourself! Some SI prefixes are almost never used because they are so small or large. A micrometer (m) is 10–6 m, while a nanometer is 10–9 m. A gigameter is 109 m. 7. a. How many nanometers are in 1 gigameter? 1 gigameter 1,000,000,000,000,000,000 nanometers
b. How many gigameters are in 1,000,000,000,000 micrometers? 1,000,000,000,000 micrometers 0.001 gigameters
A Formula for SI Catch-up Scientists use SI all the time. But most people in the United States still use non-SI units. So what do you do if you have data in non-SI units and you want to convert the data into SI units, or vice versa? Have no fear! Conversion charts, like the one shown below, can help you accomplish the task with ease. SI Conversion Chart Multiply by
inches (in.) feet (ft)
fluid ounces (fl oz)
PROCEDURE: To convert from non-SI units to SI units, find the non-SI unit in the
left column and multiply it by the number in the center column. The resulting number will be in the SI unit in the right column. To convert a SI unit into a non-SI unit, find the SI unit in the right column and divide by the number in the center column to get the non-SI unit on the left.
8 lb 0.45 kg/lb 3.6 kg; 3.6 kg 1000 g/kg 3600 g; 4 oz 28.35 g/oz 113.4 g;
Counting the Zeros A power of 10 is a number that can have 10 as its only factors. For instance, (10 10) 100 and (10 10 10 10) 10,000 are both powers of 10. Multiplying and dividing by powers of 10 is as easy as counting the zeros and moving your decimal point the same number of places.
Part 1: Multiplying by Powers of 10 PROCEDURE: To multiply a number by a power of 10, move the decimal point to
the right the same number of places as there are zeros in the power of 10. If there are not enough places in your number to do this, you will need to add zeros to the number as place holders. SAMPLE PROBLEM: Multiply 8.25 by 10, 100, and 1000.