Scientific notation writes a very large or very small number as a decimal coefficient multiplied by a power of ten:

$$a\times10^n,$$

where $n$ is an integer. In normalized scientific notation, the coefficient has exactly one nonzero digit to the left of the decimal point; a negative number keeps its minus sign in front of that coefficient.

The exponent records the scale of the number. A positive exponent moves the decimal point to the right when the number is written in ordinary decimal form, while a negative exponent moves it to the left:

$$6.02\times10^3=6020,$$

$$1.5\times10^{-4}=0.00015.$$

Conversely,

$$83,000,000=8.3\times10^7,$$

because the decimal point must move seven places to turn $8.3$ into $83,000,000$.

Powers of ten make multiplication and division especially convenient. Using the exponent laws,

$$(3\times10^4)(2\times10^{-6})=6\times10^{-2},$$

and

$$\frac{8\times10^7}{2\times10^3}=4\times10^4.$$

A result can be normalized by shifting the coefficient and compensating in the exponent. For example,

$$24\times10^5=2.4\times10^6.$$

Scientific notation separates a number's significant coefficient from its power-of-ten scale. It is therefore useful whenever quantities span many orders of magnitude, as they commonly do in physics, chemistry, engineering and biology.