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, point, 4, 9, times, 10, to the power minus 24.49×10 −2 centimeters Cell C: 2, point, 0, 6, times, 10, to the power minus 32.06×10 −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 1

To find how many times larger the diameter of cell B is compared to cell C, we first need to convert both measurements into standard notation.

For Cell B: \[ 4.49 \times 10^{-24.49} \text{ cm} = 4.49 \times 10^{-25} \text{ cm} \quad \text{(since } 10^{-24.49} = 10^{-25} \times 10^{0.51}) \] Now let's calculate: \[ \text{Value of Cell B} = 4.49 \times 10^{-25} \text{ cm} \]

For Cell C: \[ 2.06 \times 10^{-32.06} \text{ cm} = 2.06 \times 10^{-33} \text{ cm} \quad \text{(since } 10^{-32.06} = 10^{-33} \times 10^{0.94}) \] Now let's calculate: \[ \text{Value of Cell C} = 2.06 \times 10^{-33} \text{ cm} \]

Now we will divide the diameter of cell B by the diameter of cell C:

\[ \text{Ratio} = \frac{4.49 \times 10^{-25}}{2.06 \times 10^{-33}} \]

This can be simplified by separating the constants and exponential components:

\[ \text{Ratio} = \frac{4.49}{2.06} \times \frac{10^{-25}}{10^{-33}} \] \[ = \frac{4.49}{2.06} \times 10^{8} \]

Calculating \(\frac{4.49}{2.06}\): \[ \frac{4.49}{2.06} \approx 2.1767 \]

Now multiplying this by \(10^{8}\): \[ \text{Ratio} \approx 2.1767 \times 10^{8} \]

Now we round to the nearest tenth: \[ \approx 2.2 \times 10^{8} \]

Thus, the final answer, representing how many times larger the diameter of cell B is than the diameter of cell C, is: \[ \boxed{2.2 \times 10^8} \]

Answer 2

wrong

Answer 3

Let's carefully calculate how many times larger the diameter of Cell B is compared to Cell C using the given measurements.

Given Measurements

• Cell B: \( 4.49 \times 10^{-24} \) cm
• Cell C: \( 2.06 \times 10^{-32} \) cm

Calculating the Ratio

To find how many times larger Cell B is than Cell C, we need to compute: \[ \text{Ratio} = \frac{\text{Diameter of Cell B}}{\text{Diameter of Cell C}} = \frac{4.49 \times 10^{-24}}{2.06 \times 10^{-32}} \]

Step 1: Divide the Coefficients

\[ \frac{4.49}{2.06} \approx 2.1767 \]

Step 2: Subtract the Exponents

When dividing like bases in scientific notation, subtract the exponents: \[ 10^{-24} \div 10^{-32} = 10^{-24 - (-32)} = 10^{-24 + 32} = 10^{8} \]

Step 3: Combine Results

Now we combine the results from the above steps: \[ \text{Ratio} \approx 2.1767 \times 10^{8} \]

Rounding

Now, rounding \(2.1767\) to the nearest tenth gives us \(2.2\).

Final Result

Thus, the final result is: \[ \boxed{2.2 \times 10^{8}} \]

After reviewing the calculations, they are indeed correct. If there's any specific part that you believe is incorrect or if you have a different understanding of the measurements, please let me know!