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Exact and Inexact Numbers - PowerPoint PPT Presentation

Exact and Inexact Numbers. In scientific work, numbers are groups in two categories: exact numbers and inexact numbers. An exact number is a number that has a value with no uncertainty in it; that is, it is known exactly. Examples: There are exactly 12 objects in a dozen, not 12.01 or 12.02.

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Exact and Inexact Numbers

In scientific work, numbers are groups in two categories: exact numbers and inexact numbers. An exact number is a number that has a value with no uncertainty in it; that is, it is known exactly.

Examples:

There are exactly 12 objects in a dozen, not 12.01 or 12.02.

There can be 7 people in a room, but never 6.99 or 7.02.

An exact numbers and inexact numbers. An inexact number is a number that has a value with a degree of uncertainty in it. Inexact numbers result anytime a measurement is made.

It is impossible to make an exact measurement; some uncertainty will always be present.

Flaws in measuring-device construction, improper calibration of an instrument, and the skills (or lack of skills) possessed by a person using a measuring device all contribute to (uncertainty).

Errors uncertainty will always be present. in measurement can be classified as either random errors or systematic errors.

A random error is an error originating from uncontrollable variables in an experiment. Such errors result in experimental values that fluctuate about the true value. A variation in the angle from which a measurement scale is viewed will cause random error.

Momentary changes in air currents, atmospheric pressure, or temperature near a sensitive balance for weighting would cause random errors. The net result of random errors, which can never be completely eliminated, is a decrease in the precision of a series of measurements.

A uncertainty will always be present. systematic error is an error originating from controllable variables in an experiment. They are “constant” errors that occur again and again. A flaw in a piece of equipment, such as a chipped weight in a balance, would cause systematic error. All readings would be off by a specific amount because of the flaw.

Accuracy, Precision, and Error uncertainty will always be present.

Precision is an indicator of how close a series of measurements on the same object are to each other.

Accuracy uncertainty will always be present. is an indicator of how close a measurement (or the average of multiple measurements) comes to a true or accepted value.

The activity of throwing darts at a target illustrates nicely the difference between these two terms.

Accuracy refers to how close the darts are to the center (bull's-eye) of the target. Precision refers to how close the darts are to each other.

The difference between precision and accuracy. nicely the difference between these two terms.

Practice Problem nicely the difference between these two terms.

Student A: poor accuracy, poor precision

Solution

Student B: good accuracy, good precision

Student C: poor accuracy, good precision

Poor accuracy nicely the difference between these two terms.

Poor precision