Example 6.2.9

In quantum mechanics, there is an important value called the Planck Constant 3 . Written as a decimal, the value of the Planck constant (rounded to 4 significant digits) is

\begin{equation*} 0.0000000000000000000000000000000006626\text{.} \end{equation*}

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

\begin{equation*} 0.0000000000000000000000000000000006626 \end{equation*}

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