Question

think about the process. the length of cell a is (8\times10^{-5}\text{ m}). the length of cell b is (0.0000004\text{ m}). what is the ratio of cell as length to cell bs length? use pencil and paper. is it easier to find the ratio when the numbers are expressed in scientific - notation or in standard form? explain your reasoning. the ratio of cell as length to cell bs length is (square). (write the ratio as a simplified fraction.)

Explanation:

Step1: Write lengths in scientific - notation

The length of cell A is \(8\times10^{-5}\text{ m}\). The length of cell B is \(0.0000004\text{ m}=4\times 10^{-7}\text{ m}\).

Step2: Calculate the ratio

The ratio of cell A's length to cell B's length is \(\frac{8\times 10^{-5}}{4\times 10^{-7}}\).
Using the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\) and \(\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}\), we have \(\frac{8}{4}\times\frac{10^{-5}}{10^{-7}} = 2\times10^{-5-(-7)}=2\times10^{2}\).
In standard form, \(2\times10^{2}=200\), and as a fraction \(\frac{200}{1}\).

Answer:

\(\frac{200}{1}\)