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# Absolute Value Equations

## Equations may have two solutions due to the absolute value operation

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Calibration

Credit: Laura Guerin
Source: CK-12 Foundation

Have you ever heard of a measurement “having an error” of 3% or 5%? Despite all efforts to make a measuring device accurate, there’s a chance it will show results that are slightly incorrect. The difference, in terms of percentage error, is stated in the specifications of the device.

#### Why It Matters

What does a 3% error mean? It means that the absolute value of the difference between the measured and actual quantities is 3% of the actual value. You can use absolute value equations to reverse-calculate the actual quantity (or a range for it). Ideally, when a measuring device is manufactured, it is tested to ensure that it provides accurate results. For sophisticated equipment, this process is repeated periodically to ensure that any wear-off over time can be adjusted for appropriately. The pieces of equipment are “tuned” so that they start operating reliably again. This process is called calibration.

Credit: Laura Guerin
Source: CK-12 Foundation

Do you know where the definitions of a pound and a kilogram come from? A pound is now officially defined in terms of kilograms, but what about the kilogram? Unlike the absolute definitions of “second,” “meter,” etc., “kilogram” is the only standard unit that is defined by a physical object rather than a fundamental physical property. This artifact is called the International Prototype of the Kilogram (IPK), and it is held by the International Bureau of Weights and Measures, located in France. But unique problems can arise when the world relies on a particular object to define a unit. As it turned out a few years ago, the IPK is vulnerable to defects as well-so the very definition of kilogram has needed some calibration!

Watch the following video to see the lengths these international standards organizations have gone to maintain a proper definition for the kilogram:

#### Explore More

Suppose you’re weighing yourself on a used scale you just bought. The seller told you that it’s defected and that the scale is about 5% off. If the scale shows that you’re 152 lbs, how much do you really weigh?

Credit: Bill Branson/NIH
Source: http://commons.wikimedia.org/wiki/File:Feet_on_scale.jpg

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