Question 13

There are approximately 2.5 X 10^5 amoebas in a sample that weighs 1 gram.

To find the number of amoebas in a 1-gram sample, we divide 1 gram by the mass of a single amoeba, which is 4.0 X 10^(-6) grams. This calculation yields approximately 2.5 X 10^5 amoebas.

A) 2.5 X 10^5

This option is correct because when calculating the number of amoebas in a 1-gram sample, we divide 1 gram by 4.0 X 10^(-6) grams per amoeba. Performing this division, 1 / (4.0 X 10^(-6)) results in 2.5 X 10^5 amoebas.

B) 4.0 X 10^7

This option is incorrect because it suggests that there are significantly more amoebas than the calculated amount. If we divide 1 gram by 4.0 X 10^(-6) grams, we do not arrive at 4.0 X 10^7; instead, the calculations show a lower number of amoebas.

C) 4.0 X 10^5

This option is incorrect as well. The value of 4.0 X 10^5 amoebas would imply a different mass per amoeba than what is given. The correct calculation leads to a result that is an order of magnitude lower than this option.

D) 2.5 X 10^7

This option is also incorrect. The calculation of the number of amoebas based on their mass does not support this higher figure. The result obtained from the proper division is significantly less than 2.5 X 10^7.

Conclusion

The correct answer, 2.5 X 10^5, accurately represents the number of amoebas in a 1-gram sample based on their mass of 4.0 X 10^(-6) grams each. All other options fail as they either overestimate or miscalculate the number of amoebas based on the given mass, demonstrating a misunderstanding of the relationship between mass and quantity in this context.