Question

These exercises involve scientific notation.

Write the number $2.08\times {10}^{-8}$in ordinary decimal notation.

Short answer

The ordinary decimal notation of$2.08\times {10}^{-8}$ is $0.0000000208$.

Step-by-step solution

Step 1. Definition of scientific notation.

Scientific notation is a method to rewrite a large number in terms of a decimal number between$1$ and$10$ multiplied by a power of $10$.

For example: The scientific notation of$75000$ is $7.5\times {10}^4$.

Step 2. Given Information.

The given scientific notation of a number is $2.08\times {10}^{-8}$.

Step 3. Scientific notation of the given number.

The given number can be rewritten as:

$\begin{array}{c}2.08\times {10}^{-8}=2.08\times \frac{1}{{10}^8}\left[\because a^{-n}=\frac{1}{a^n}\right]\\ =\frac{2.08}{100,000,000}\\ =0.0000000208\end{array}$

Thus, the ordinary decimal notation of$2.08\times {10}^{-8}$ is $0.0000000208$.