Scientific Notation
Scientific notation is a way of writing numbers that are very large or very small in a compact and convenient form. It is widely used in the sciences, engineering, and mathematics, and is especially useful for dealing with numbers that have a lot of zeros.
scientific notation
In scientific notation, a number is written as a product of two parts: a coefficient and a power of [latex]10[/latex].
It is written in the form [latex]a\times {10}^{n}[/latex], where [latex]1\le |a|<10[/latex] and [latex]n[/latex] is an integer. [latex]n[/latex] can be positive or negative depending on whether a small or large number is being converted to scientific notation.
Although scientific notation can look confusing, we can follow a few simple steps to convert numbers in standard notation to scientific notation.
- Count the number of places that the decimal point needs to be moved to the right or left so that the coefficient is between [latex]1[/latex] and [latex]9[/latex].
- Move the decimal point the appropriate number of places to the right or left, and adjust the power of [latex]10[/latex] accordingly.
- Write the result as the coefficient followed by [latex]x 10^n[/latex], where [latex]n[/latex] represents the number of times that the decimal point was moved.
Remember the sign on [latex]n[/latex] depends on if you are converting a small or large number to scientific notation. A rule to remember is if you move your decimal to the left [latex]n[/latex] is positive and if you move your decimal to the right [latex]n[/latex] is negative.
To convert from scientific notation to standard notation, we simply need to do the reverse of the steps given before.
- Write the coefficient and the power of [latex]10[/latex] separately.
- Move the decimal point in the coefficient the same number of places to the left or right as the power of [latex]10[/latex] suggests.
- Combine the coefficient and the decimal point to get the standard notation representation of the number.