# 0.7 Phy1040: scientific notation and significant figures  (Page 2/8)

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## General background information

This section will contain a discussion of accuracy, precision, scientific notation, and significant figures.

## Accuracy and precision

Let's begin with a brief discussion of accuracy and precision. These two terms are often confused in everyday conversation, but they have very differentmeanings in the world of science and engineering.

Accuracy

In science and engineering, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to its actual (true) value.

Precision

The precision of a measurement system (also called reproducibility or repeatability) is the degree to which repeated measurements under unchangedconditions show the same result.

Four possibilities

A measurement system can be:

• Both accurate and precise.
• Accurate but not precise.
• Precise but not accurate.
• Neither accurate nor precise.

A hypothetical experiment

Consider an experiment where a firearm is clamped into a fixture, very carefully aimed at a bulls eye on a downrange target, and fired six times.(Although you may never have seen or touched a firearm, you probably have a pretty good idea of how they behave.)

If the six holes produced by the bullets in the target fall in a tight cluster in the bulls eye, the system can be considered to be both accurate andprecise.

If all of the holes fall in the general area of the bulls eye but the cluster is not very tight, the system can be considered to be accurate but not precise.

If all of the holes fall in a tight cluster but the cluster is some distance from the bulls eye, the system can be considered to be precise but not accurate.

If the holes are scattered across a wide area of the target, the system can be considered to be neither accurate nor precise.

Another use of the word precision

Another use of the word precision, which will be important in this module, is based on the concept that the precision of a measurement describes the unitsthat you use to measure something.

How tall are you?

For example, if you tell someone that you are about five feet tall, that wouldn't be very precise. If you told someone that you are 62 inches tall, thatwould be more precise. If you told someone that you are 62.3 inches tall, that would be even more precise, and if you told someone that you are 62.37 inchestall, that would be very precise for a measurement of that nature.

The smaller the unit...

The smaller the unit you use to measure with, the more precise the measurement can be. For example, assume that you measure someone's height with atactile measuring stick that is longer than the person is tall. Assume also that the measuring stick is graduated only in feet. In that case, the best that youcould hope for would be to get the measurement correct to the nearest foot and perhaps estimate a second digit to the nearest tenth of a foot.

On the other hand, if the measuring stick is graduated in inches and you are careful, you should be able to get the measurement correct to the nearest inchand perhaps estimate another digit to the nearest tenth of an inch. The second measurement using the one-inch graduations would be more precise than the firstusing the one-foot graduations.

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in general
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