Question

the length of a particular bacteria cell is 1.6×10^(-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? 1. 56 times larger 2. 5.6 times larger 3. 14.4 times larger 4. 144 times larger

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. The length of the bacteria cell is $1.6\times10^{-7}$ meters and the length of the red - blood cell is $9\times10^{-6}$ meters. The division is $\frac{9\times 10^{-6}}{1.6\times 10^{-7}}$.

Step2: Separate coefficients and exponents

Using the rule $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $\frac{9}{1.6}\times10^{-6-(-7)}$.

Step3: Calculate the coefficient part

$\frac{9}{1.6}=5.625$.

Step4: Calculate the exponent part

$10^{-6-(-7)} = 10^{-6 + 7}=10^{1}=10$. But since the coefficient part is already a non - power - of - 10 number, the result is just 5.625 times larger.

Answer:

5.625 times