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# 1.7: Conversion of Units

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### 1.7: Conversion of Units

Sometimes, there is a need to convert from one unit to another one. For instance, reading a cookbook in which quantities are expressed in units of liters or ounces may require conversion of quantities to cups. Or, when looking up directions on how to get to a location, we may be interested to know how many miles we are going to walk. In this case, we would have to convert units of feet or meters to miles.

The first step in the unit conversion is to list the given units and the units required for the conversion. The second step is to determine a conversion factor relating to the given and required unit. The conversion factor is defined as the ratio that expresses how many of one unit is equal to another unit. For example, there are 1,000 meters in 1 kilometer. While doing a conversion, ensure that the units in the unit conversion cancel correctly.

One well-known example of the significance of unit conversion is the Mars Climate Orbiter. NASA launched this probe on December 11, 1998. However, on September 23, 1999, NASA lost contact with the probe while attempting to guide it into its planned orbit around Mars. Subsequent investigations revealed that the units in the two programs used to record and drive the thruster were out of sync. This error caused the probe to follow a very different trajectory than the one that NASA projected, causing it to burn up in the Martian atmosphere or shoot out into space. This failure to pay attention to unit conversions cost hundreds of millions of dollars, not to mention the time spent on the project by the scientists and engineers.

This text is adapted from Openstax, University Physics Volume 1, Section 1.3: Unit Conversion.

#### Tags

Unit Conversion Convert Units Conversion Factor Given Units Required Units Cookbook Quantities Cups Miles Feet Meters Mars Climate Orbiter NASA Probe Orbit Trajectory Error

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