The mass of an amoeba is approximately $4.0 \times 10^{-6}$ grams. Which of the following is closest to the number of amoebas in 1 gram?
A. $2.5 \times 10^5$
B. $4.0 \times 10^5$
C. $4.0 \times 10^7$
D. $2.5 \times 10^7$
Answer (2)
The mass of one amoeba is approximately 4.0 × 1 0 − 6 grams.
Set up the equation N × ( 4.0 × 1 0 − 6 ) = 1 , where N is the number of amoebas.
Solve for N : N = 4.0 × 1 0 − 6 1 = 2.5 × 1 0 5 .
The approximate number of amoebas with a combined mass of 1 gram is 2.5 × 1 0 5 .
Explanation
Understanding the Problem We are given that the mass of one amoeba is approximately $4.0
\times 10^{-6}$ grams. We want to find the approximate number of amoebas that would have a combined mass of 1 gram.
Setting up the Equation Let N be the number of amoebas. The total mass of N amoebas is $N
\times (4.0 \times 10^{-6})$ grams. We want the total mass to be 1 gram, so we set up the equation:
N × ( 4.0 × 1 0 − 6 ) = 1
Solving for N To solve for N , we divide both sides of the equation by 4.0 × 1 0 − 6 :
N = 4.0 × 1 0 − 6 1
N = 4.0 1 × 1 0 6
N = 0.25 × 1 0 6
N = 2.5 × 1 0 5
Final Answer Therefore, the approximate number of amoebas that would have a combined mass of 1 gram is 2.5 × 1 0 5 .
Examples
Imagine you're a biologist studying microorganisms. You know the average mass of one amoeba and want to estimate how many amoebas you'd need to collect to have a sample weighing one gram. This calculation helps you plan your experiment and understand the scale of the microbial world. This type of estimation is also useful in environmental science when assessing the biomass of microorganisms in a soil or water sample.
The number of amoebas in 1 gram is approximately 2.5 × 1 0 5 . We found this by dividing 1 gram by the mass of a single amoeba, 4.0 × 1 0 − 6 grams. Therefore, the correct answer is option A: 2.5 × 1 0 5 .
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