2.4 Game 2302-0340 scientific notation and significant figures  (Page 3/7)

A power of ten is understood

In this format, it is understood that the number consists of the value to the left of the e (the mantissa) multiplied by ten raised to a power given by the value to the right of the e (the exponent).

For example, in JavaScript exponential format, the value -10*Math.PI is displayed as

-3.141592653589793e+1

The value Math.PI/10 is displayed as

3.141592653589793e-1

The value Math.PI is displayed as

3.141592653589793e+0

The value 0 is displayed as

0e+0

The normalized form of scientific notation

Using general scientific notation, the number -65700 could be writtenin several different ways including the following:

• -6.57 * 10^4
• -65.7 * 10^3
• -657 * 10^2

In normalized scientific notation, the exponent is chosen such that the absolute value of the mantissa is at least one but less than ten. For example, -65700 is written:

-6.57 * 10^4

In normalized notation the exponent is negative for a number with absolute value between 0 and 1. For example, the value 0.00657 would be written:

6.57 * 10^(-3)

The 10 and the exponent are usually omitted when the exponent is 0.

Significant figures

According to Wikipedia , The significant figures of a number are those digits that carry meaning contributing to its precision. This includes all digits except:

• Leading zeros where they serve merely as placeholders to indicate the scale of the number (.00356 for example).
• Spurious digits introduced, for example, by calculations carried out to greater accuracy than that of the original data, or measurements reported to a greater precision than the equipment supports.

A popular physics textbook provides a more complete set of rules for identifying the significant figures in a number:

1. Nonzero digits are always significant.
2. Final or ending zeros written to the right of the decimal point are significant.
3. Zeros written to the right of the decimal point for the purpose of spacing the decimal point are not significant.
4. Zeros written to the left of the decimal point may be significant, or they may only be there to space the decimal point. For example, 200 cm could have one,two, or three significant figures; it's not clear whether the distance was measured to the nearest 1 cm, to the nearest 10 cm, or to the nearest 100 cm. Onthe other hand, 200.0 cm has four significant figures (see rule 5). Rewriting the number in scientific notation is one way to remove the ambiguity.
5. Zeros written between significant figures are significant.

Ambiguity of the last digit in scientific notation

Again, according to Wikipedia , it is customary in scientific measurements to record all the significant digits from the measurements, and to guess one additional digit if there is any information at all available to the observer to make a guess. The resulting number is considered more valuable than it would be without that extra digit, and it is considered a significant digit because it contains some information leading to greater precision in measurements and in aggregations of measurements (adding them or multiplying them together).