# Scientific Notation

Scientific notation is a tool that uses powers to simplify handling numbers that are very big or very small, such as 0.00000057.

This number could also be expressed as 5.7 x 10^{-7}

A value in scientific notation is usually written as a number between 1 and 10 multiplied by 10 raised to a power.

For example, $$ \newcommand{\ctext}[1]{\style{font-family:Arial}{\text{#1}}} \begin{align*}100\ctext{ (standard notation)} &= 10^2 \cr &= 1 \times 10^2 \ctext{ (scientific notation)} \cr &= 1 \times 10 \times 10 \cr &= 100 \end{align*} $$

A number in scientific notation has two parts. The first part, that is, a number between 1 and 10, is sometimes called the coefficient. The second part is 10 raised to some power, the exponential term.

For example, 5000 = 5 x 10^{3}

In this case, 5 would be the coefficient, and 10^{3} is the second part therefore the exponential term.

Further, a negative exponent is used for a number less than one. For example,

$$ \begin{align*} 1 \times 10^{-5} &= \frac{1}{10 \times 10 \times 10 \times 10 \times 10} \cr &= \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \cr &= \frac{1}{100000} \cr &= 0.00001 \end{align*} $$

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