Question

think about the process the length of cell a is 8×10⁻⁷ m. the length of cell b is 0.00000004 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 . (type the ratio as a simplified fraction.)

Explanation:

Step1: Write cell B's length in scientific - notation

The number \(0.00000004 = 4\times10^{-8}\) m.

Step2: Calculate the ratio of cell A's length to cell B's length

The length of cell A is \(8\times 10^{-7}\) m and the length of cell B is \(4\times 10^{-8}\) m. The ratio \(\frac{8\times 10^{-7}}{4\times 10^{-8}}\). Using the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\) and \(\frac{a}{b}\), we have \(\frac{8}{4}\times10^{-7-(-8)} = 2\times10^{1}=20\). As a fraction, it is \(\frac{20}{1}\).

Step3: Discuss the ease of using scientific - notation

It is easier to find the ratio when the numbers are expressed in scientific notation. In scientific notation, we can use the rules of exponents for multiplication and division easily. For example, when dividing numbers in scientific notation \(\frac{a\times10^m}{b\times10^n}=\frac{a}{b}\times10^{m - n}\). In standard form, \(8\times10^{-7}=0.0000008\) and \(0.00000004\), and dividing \(0.0000008\div0.00000004\) requires more care with decimal - point placement.

Answer:

\(\frac{20}{1}\)