2.4 Game 2302-0340 scientific notation and significant figures  (Page 2/7)

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 ameasuring 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.

One-inch graduations

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.

Diminishing returns

If the measuring stick were graduated in tenth-inch units, however, that may or may not lead to a more precise measurement. That would beapproaching the point of diminishing returns where your inability to take full advantage of the more precise graduations and the inability of the subject toalways stand with the same degree of rigidity might come into play.

Scientific notation

According to Wikipedia , scientific notation is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation . The notation has a number of useful properties and is commonly used by scientists and engineers.A variation of scientific notation is also used internally by computers.

Scientific notation format

Numbers in scientific notation are written using the following format:

x * 10^y

which can be read as the value x multiplied by ten raised to the y power where y is an integer and x is any real number. (Constraints are placed on the value of x when using the normalized form of scientific notation which I will explain below.)

The values for x and y can be either positive or negative.

The term referred to as x is often called the significand or the mantissa .

The computer display version of scientific notation

Because of difficulties involved in displaying superscripts in the output of computer programs, a typical display of a number in scientific notation by acomputer program might look something like the following example:

-3.141592653589793e+1

where

• either numeric value can be positive, negative, or zero,
• the number of digits in the numeric value to the left of the e (the mantissa) may range from a few to many, and
• the e may be either upper-case or lower-case depending on the computer and the program.