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SI Units and Dimensional Analysis

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Dimensional Analysis

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SI Units and Dimensional Analysis


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You will learn the importance of SI units and you will complete conversions between various units by using dimensional analysis.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Describe the importance of using SI units.
  • Recognize the SI unit of measurement for length, mass, time, and electric current.
  • Recognize the SI unit of measurement for temperature, luminous intensity, and amount of substance.
  • Identify equal quantities with different units in order to determine the conversion factor for a dimensional analysis.
  • Use dimensional analysis to convert units.

Everything You'll Have Covered

The International System of Units (SI) was established in 1960 in order to provide a basis for units of measurement. It is comprised of seven base quantities and units: electric current (ampere), length (meter), luminous intensity (candela), mass (kilogram), temperature (kelvin), amount of substance (mole), and time (second). These base units are mutually exclusive of each other. One of the many advantages of this system is that it is not static. Base units can be combined to form derived units as needed. Without a standard system of units, it is much more difficult to compare measurements.

The units were chosen for a variety of reasons. A temperature of 0 kelvin is the theoretical complete absence of heat, the equivalent of -273.15 C, and kelvin does not include a degree symbol. A mole refers to the amount of elementary particles found in a substance. The ampere measures the amount of charge passing some point every second. The meter was originally designated as one ten-millionth of the distance from the Equator to the North Pole, but has since been redefined as the distance traveled by light in a vacuum in 1/299,792,458 of a second. The kilogram was initially defined as the mass of 1 liter of water. The second was originally established as a fraction of a solar day but has since changed to a more precise atomic standard. The unit for luminous intensity varied among different countries, before the standard unit known as the candela was adopted.

Additionally, the metric system is incorporated into the International System which allows scientists to take advantage of the common prefixes, such as "kilo," "centi," and "milli." The prefix, "kilo," has a value of 1,000 or 10^3. "Centi" has a value of 0.01 or 10^-2, and "milli" has a value of 0.001 or 10^-3. Some of the advantages to including the metric system are that most of the world uses this system in measurements and the prefix values allow for simple conversions.

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Students should be familiar with division skills, fractions, and multiplication skills.
Course Physics
Type of Tutorial Math in Science
Key Vocabulary dimensional analysis, metric prefixes, SI units