A scientist reviews her data to find the measures of central tendency using a calculator.

She finds the average mass of an adult brown bear is about 1.36E5 grams, and the average mass of a beetle fly is approximately 0.61E2 grams.

She also found the sum total of her data using a calculator. The total brown bear population in the world is approximately 2E5, and the total beetle fly population is approximately 7E10.

Rounded to the nearest whole number, the total mass of all living beetle flies is approximately Blank times more than the total mass of all living brown bears.

1 answer

To find out how many times more the total mass of all living beetle flies is compared to the total mass of all living brown bears, we need to first calculate the total mass of each population.

  1. Total mass of brown bears:

    • Average mass of a brown bear = \( 1.36 \times 10^5 \) grams
    • Total population of brown bears = \( 2 \times 10^5 \)

    Total mass of brown bears = \( (1.36 \times 10^5) \times (2 \times 10^5) \)

    \[ = 1.36 \times 2 \times 10^{5+5} = 2.72 \times 10^{10} \text{ grams} \]

  2. Total mass of beetle flies:

    • Average mass of a beetle fly = \( 0.61 \times 10^2 \) grams
    • Total population of beetle flies = \( 7 \times 10^{10} \)

    Total mass of beetle flies = \( (0.61 \times 10^2) \times (7 \times 10^{10}) \)

    \[ = 0.61 \times 7 \times 10^{2+10} = 4.27 \times 10^{12} \text{ grams} \]

  3. Calculate how many times the total mass of beetle flies is greater than the total mass of brown bears:

    We need to divide the total mass of beetle flies by the total mass of brown bears:

    \[ = \frac{4.27 \times 10^{12}}{2.72 \times 10^{10}} \]

    To perform this calculation:

    \[ = \left( \frac{4.27}{2.72} \right) \times \left( \frac{10^{12}}{10^{10}} \right) = \frac{4.27}{2.72} \times 10^{2} \]

    Now, calculating \( \frac{4.27}{2.72} \):

    \[ \approx 1.57 \]

    Therefore,

    \[ \approx 1.57 \times 10^{2} = 157 \]

Rounded to the nearest whole number, the total mass of all living beetle flies is approximately 157 times more than the total mass of all living brown bears.