###### Example6.1.27

In quantum mechanics, there is an important value called the Planck Constant. Written as a decimal, the value of the Planck constant (rounded to 4 significant digits) is $$0.0000000000000000000000000000000006626\text{.}$$

In scientific notation, this number will be $$6.626\times 10^{\mathord{?}}\text{.}$$ To determine the exponent, we need to count the number of places from where the decimal is when the number is written as $$0.0000000000000000000000000000000006626$$ to where it will be when written in scientific notation:

\begin{equation*} 0\overbrace{.\highlight{0000000000000000000000000000000006}}^{34\text{ places}}626 \end{equation*}

As a result, in scientific notation, the Planck Constant value is $$6.626 \times 10^{-34}\text{.}$$ It will be much easier to use $$6.626 \times 10^{-34}$$ in a calculation, and an added benefit is that scientific notation quickly communicates both the value and the order of magnitude of the Planck constant.

in-context