Question

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 h: $9.47 \times 10^{-3}$ centimeters
cell k: $8.5 \times 10^{-4}$ centimeters
how many times larger is the diameter of cell h than the diameter of cell k? write your answer in standard notation, rounding to the nearest tenth.
answer
attempt 1 out of 2
answer:

Explanation:

Step1: Divide the diameter of Cell H by that of Cell K

To find how many times larger the diameter of Cell H is than Cell K, we divide the diameter of Cell H by the diameter of Cell K. So we have the expression: $\frac{9.47 \times 10^{-3}}{8.5 \times 10^{-4}}$

Step2: Use the rule of exponents for division

When dividing numbers in scientific notation, we can separate the coefficients and the powers of 10. For the coefficients, we do $9.47\div8.5$, and for the powers of 10, we use the rule $a^m\div a^n=a^{m - n}$, so $10^{-3}\div10^{-4}=10^{-3-(-4)} = 10^{1}$.

First, calculate $9.47\div8.5\approx1.114$. Then multiply by $10^{1}$ (which is 10), so $1.114\times10 = 11.14$.

Step3: Round to the nearest tenth

Rounding 11.14 to the nearest tenth, we look at the hundredth place, which is 4. Since 4 < 5, we round down, so we get 11.1.

Answer:

11.1