Question

These exercises involve scientific notation.

If $a\approx 0.00000293,b\approx 1.582\times {10}^{-14}$, and $c\approx 2.8064\times {10}^{12}$use a calculator to approximate the number $\frac{ab}{c}$.

Short answer

The approximate value of$\frac{ab}{c}$ is $1.65167\times {10}^{-32}$.

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 values are:

$\begin{array}{l}a\approx 0.00000293\\ b\approx 1.582\times {10}^{-14}\\ c\approx 2.8064\times {10}^{12}\end{array}$

Step 3. Find the required value.

Write the value of in scientific notation.

$\begin{array}{c}a\approx \frac{2.93}{1,000,000}\\ a\approx 2.93\times {10}^{-6}\end{array}$

Now, find the value of $\frac{ab}{c}$.

$\begin{array}{c}\frac{ab}{c}=\frac{\left(2.93\times {10}^{-6}\right)\left(1.582\times {10}^{-14}\right)}{2.8064\times {10}^{12}}\\ =\frac{\left(2.93\times 1.582\right)\left({10}^{-6}\times {10}^{-14}\right)}{2.8064\times {10}^{12}}\\ =\frac{4.63526\times {10}^{-20}}{2.8064\times {10}^{12}}\\ =1.65167474344\times {10}^{-32}\\ \approx 1.65167\times {10}^{-32}\end{array}$

Thus, the approximate value of$\frac{ab}{c}$ is $1.65167\times {10}^{-32}$.