Unit Of Volume

Data, Measurement, and Units Exercise
Objectives:

Name ___________________________________ (adapted from the oceanography lab manuals by RE Johnson and by HV Thurman & SM Savin)

* Define and relate the terms unit, measurement, and data. * Measure height, width, and length of an object in both English and metric systems, calculating the object's volume, as well as the percent deviation ofmeasurements. * Define the term conversion factor and be able to give examples. * Perform simple and multiple unit conversions, both within the metric system and between the English and metric systems. * State and apply the rules for identifying the significant figures in a number. * Round off calculations to the correct number of significant figures. * State the rules for scientific notation anddefine the term exponent. * Translate between regular notation and scientific notation. * Perform, without a calculator, operations of addition, subtraction, multiplication, and division using scientific notation. * Solve equations for a given variable and attain a final numerical value. * Apply these techniques to examples relevant to geology

Introduction:
All physical quantities can befundamentally expressed in terms of units of length, mass, and time. A unit, such as an inch, pound, or second, is an amount or quantity that serves as a standard against which other quantities are compared or measured. An accompanying numerical value relates the magnitude, or size, of any measurement to that standard. Thus, a measurement has two essential parts: a number and a unit. Examples ofmeasurements are 12 feet, 16 pounds, and 60 minutes. It is important to remember that the expression of any measurement in terms of only a numerical value is incomplete. For example, the number 8.5 alone does not express the width of this page. The numerical value, 8.5, and the unit of measurement, inches, must both be specified. A collection or series of measurements is referred to as data. Scientificdata are typically measured and recorded using the metric system of units because of the simplicity of converting among units. However, because the English (British) system of units is still prevalent in everyday life in the United States, the scientist must be familiar with the relationships between the two systems and be able to easily convert, or switch, units when necessary.

The MetricSystem:
A working proficiency in using the metric system can be attained by simply learning three base units and a few prefixes:

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Base unit meter gram liter Prefix giga mega kilo centi milli micro nano

Quantity length mass volume

Abbreviation m g L Abbreviation G M k c m µ n In Scientific Notation 109 (billions) 106 (millions) 103 (thousands) 10-2 (one-hundredth) 10-3(one-thousandth) 10-6 (one-millionth) 10-9 (one-billionth)

Definition 1,000,000,000 times the base unit 1,000,000 times the base unit 1000 times the base unit 1/100 of the base unit 1/1000 of the base unit 1/1,000,000 of the base unit 1/1,000,000,000 of the base unit

By combining a prefix and a base unit, a new unit that has a known relationship to the base unit is formed. For example: Prefix kilo (k)centi (c) + + + Base Unit meter (m) meter (m) ! ! ! New Base Unit 1000 m = 1 km 1/100 m = 0.01 m = 1 cm

Converting Units:
Often it is necessary to change the unit of a measurement to a different unit, of either the same or a different system. To convert a unit, the "conversion factor" must be known. A conversion factor is the relationship between the old unit and the new unit. For example, toconvert from feet to inches, the conversion factor, 12 inches = 1 foot, is necessary. Table 1 lists some commonly used conversion factors, both within the metric system and between the metric and English systems. Consider units as algebraic quantities that may be multiplied or divided by one another. In converting units, we can take advantage of three facts: 1. Multiplying or dividing anything by...