Page 31 - Laboratory Manual in Physical Geology

Calculators display a limited number of decimal Unit Conversion—The Math You Need
places, so numbers with many decimal places must be You can learn more about unit conversion
entered in exponential notation. The calculators on (including practice problems) at this site
many “smart phones” will display many decimal places featuring The Math You Need, When
when held horizontally. But if you turn the phone to You Need It math tutorials for students in
a vertical position (with less space to display decimal introductory geoscience courses: http://serc.
places), then the phone will automatically change the carleton.edu/mathyouneed/units/index.html
number to exponential notion. Smart phones and most
calculators use an “E” to signify the exponent, so one Area and Volume
billion would be displayed as something like “1e+9”
9
(representing 1 * 10 ). An area is a two-dimensional space, such as the surface
The International System of Units (SI) is the modern of a table. The long dimension is the length , and the
version of the metric system and is based on powers of short dimension is the width . If the area is square or
ten. See page xi at the front of this manual to learn more rectangular, then the size of the area is the product of its
about it and how scientific notation is used to express large length multiplied times its width. For example, the blue

metric units. rectangular area in FIGURE 1.8A is 7.3 cm long and 3.8 cm
wide. So the size of the area is 7.3 cm * 3.8 cm , which

2

Linear Measurements and Conversions equals 27.7 cm . This is called 27.7 square centimeters.
Using this same method, the yellow front of the box in
You must be able to use a metric ruler to make exact FIGURE 1.8B has an area of 9.0 cm * 4.0 cm, which equals

measurements of length (how long something is). This 36.0 cm . The green side of this same box has an area of
2

is called linear measurement . Most rulers in the United 4.0 cm * 4.0 cm, which equals 16.0 cm .
2
States are graduated in English units of length (inches) Three-dimensional objects are said to occupy a
on one side and metric units of length (centimeters) on volume of space. Box shaped objects have linear volume
the other. For example, notice that one side of the ruler because they take up three linear dimensions of space:

in FIGURE 1.8A is graduated in numbered inches, and each their length (longest dimension), width (or depth), and

inch is subdivided into eighths and sixteenths. The other height (or thickness). So the volume of a box shaped
side of the ruler is graduated in numbered centimeters object is the product of its length, width, and height. For
(hundredths of a meter), and each centimeter is subdivided example, the box in FIGURE 1.8B has a length of 9.0 cm,

into ten millimeters. The ruler provided for you in a width of 4.0 cm, and a height of 4.0 cm. Its volume is
GeoTools Sheets 1 and 2 at the back of this manual are 9.0 cm * 4.0 cm * 4.0 cm, which equals 144 cm . This
3
graduated in exactly the same way. is read as “144 cubic centimeters.”
Review the examples of linear metric measurement Most natural materials such as rocks do not have
in FIGURE 1.8A to be sure that you understand how to linear dimensions, so their volumes cannot be calculated

make exact metric measurements. Note that the length of from linear measurements. However, the volumes of these
an object may not coincide with a specific centimeter or odd-shaped materials can be determined by measuring
millimeter mark on the ruler, so you may have to estimate the volume of water they displace. This is often done in
the fraction of a unit as exactly as you can. The length of the laboratory with a graduated cylinder ( FIGURE 1.8C ),
the red rectangle in FIGURE 1.8A is between graduation an instrument used to measure volumes of fluid (fluid
marks for 106 and 107 millimeters (mm), so the most volume). Most graduated cylinders are graduated in metric
exact measurement of this length is 106.5 mm. Also be units called milliliters (mL or ml), which are thousandths
sure that you measure lengths starting from the zero point of a liter. You should also note that 1 mL of fluid volume is
on the ruler and not from the end of the ruler . exactly the same as 1 cm of linear volume.
3

There will be times when you will need to convert When you pour water into a graduated cylinder, the
a measurement from one unit of measure to another. surface of the liquid is usually a curved meniscus , and the
This can be done with the aid of the mathematical volume is read at the bottom of the curve ( FIGURE 1.8C :
conversions chart on page xii at the front of the manual. middle and left-hand examples). In some plastic graduated
For example, to convert millimeters (mm) to meters (m), cylinders, however, there is no meniscus. The water level is
divide the measurement in mm by 1000 (because there flat ( FIGURE 1.8C : right-hand example).
are 1000 millimeters per meter):
If you drop a rock into a graduated cylinder full of
water, then it takes up space previously occupied by water at
106.5 mm
= 0.1065 m the bottom of the graduated cylinder. This displaced water
1000 mm/m
has nowhere to go except higher into the graduated cylinder.
Thus, 106.5 millimeters is the same as 0.1065 meters. Therefore, the volume of an object such as a rock is exactly
the same as the volume of fluid (water) that it displaces.
16 ■ L ABOR ATORY 1