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