Question

directions: type the correct answer in each box. spell all words correctly, and use numerals instead of words for numbers. if necessary, use / for the fraction bar(s). a scientist measures the diameter of a bacteria cell and yeast cell. she finds the diameter of a bacteria cell to be 0.0000021 meters and the diameter of a yeast cell to be 0.00000398 meters. the approximate diameter of the bacteria cell is represented by point on the number line. the approximate diameter of the yeast cell is represented by point on the number line. the diameter of the bacteria cell is approximately times smaller than the diameter of the yeast cell.

Explanation:

Step1: Convert bacteria cell diameter to scientific - notation

The diameter of the bacteria cell is $0.0000021$ meters. In scientific - notation, it is $2.1\times10^{-6}$ meters. Since $2\times10^{-6}<2.1\times10^{-6}<3\times10^{-6}$, it is represented by point B on the number line.

Step2: Convert yeast cell diameter to scientific - notation

The diameter of the yeast cell is $0.00000398$ meters. In scientific - notation, it is $3.98\times10^{-6}$ meters. Since $3\times10^{-6}<3.98\times10^{-6}<4\times10^{-6}$, it is represented by point D on the number line.

Step3: Calculate the ratio of the diameters

To find how many times smaller the bacteria cell diameter is than the yeast cell diameter, we divide the diameter of the bacteria cell by the diameter of the yeast cell. $\frac{2.1\times 10^{-6}}{3.98\times 10^{-6}}=\frac{2.1}{3.98}\approx0.53$. So the bacteria cell diameter is approximately $\frac{1}{2}$ times smaller than the yeast cell diameter.

Answer:

B
D
$\frac{1}{2}$