Question

the size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter. two cells are measured using this method: cell b: $4.49 \times 10^{-2}$ centimeters cell c: $2.06 \times 10^{-3}$ centimeters how many times larger is the diameter of cell b than the diameter of cell c? write your answer in standard notation, rounding to the nearest tenth. answer attempt 1 out of 3 standard notation

Explanation:

Step1: Divide Cell B's diameter by Cell C's diameter

To find how many times larger Cell B's diameter is than Cell C's, we divide the diameter of Cell B by the diameter of Cell C. So we have the expression: $\frac{4.49 \times 10^{-2}}{2.06 \times 10^{-3}}$

Step2: Use the rule of exponents for division

When dividing numbers in scientific notation, we divide the coefficients and subtract the exponents of 10. So, $\frac{4.49}{2.06} \times 10^{-2 - (-3)}$

Step3: Calculate the coefficient and the exponent

First, calculate $\frac{4.49}{2.06} \approx 2.1796$ (rounded to four decimal places). Then, calculate the exponent: $-2 - (-3) = -2 + 3 = 1$. So now we have $2.1796 \times 10^{1}$

Step4: Convert to standard notation

$10^{1}=10$, so $2.1796 \times 10 = 21.796$

Step5: Round to the nearest tenth

Rounding 21.796 to the nearest tenth gives 21.8

Answer:

21.8