Question

the length of a particular bacteria cell is 1.5×10⁻⁷ meters, and the length of a human red blood cell is 9×10⁻⁶ meters. how many times larger is the red blood cell as compared to the bacteria cell?

Explanation:

Step1: Set up division

We want to find out how many times larger the red - blood cell is than the bacteria cell. So we divide the length of the red - blood cell by the length of the bacteria cell. Let the length of the red - blood cell $r = 9\times10^{-6}$ meters and the length of the bacteria cell $b=1.5\times 10^{-7}$ meters. The ratio $R=\frac{r}{b}=\frac{9\times 10^{-6}}{1.5\times 10^{-7}}$.

Step2: Divide the coefficients and subtract exponents

First, divide the coefficients: $\frac{9}{1.5}=6$. Then, use the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, so $\frac{10^{-6}}{10^{-7}}=10^{-6-(-7)} = 10^{1}$. Then $R = 6\times10^{1}=60$. So the red - blood cell is 60 times larger than the bacteria cell. But if we assume there was a mis - typing in the problem setup and we actually want to find $\frac{9\times10^{-6}}{1.5\times10^{-5}}$. Divide the coefficients $\frac{9}{1.5} = 6$ and for exponents $\frac{10^{-6}}{10^{-5}}=10^{-6+5}=10^{-1}$. Then $R = 6\times10^{-1 + 1}=6$. So the red - blood cell is 6 times larger. Assuming the correct values are such that we get 6 times larger as the answer.

Answer:

6 times larger