Final answer:
To find how many times greater the state's population of 8th graders is compared to Park Crest Middle School, we round the numbers to the nearest power of ten and then calculate the ratio, resulting in the state being approximately 2000 times greater, corresponding to choice D) 2x10³.
Step-by-step explanation:
The question involves estimating powers of ten to compare the population of 8th graders at Park Crest Middle School to that of the entire state. To estimate the factor by which the state's population of 8th graders is greater than Park Crest Middle School's, we will round the populations to the nearest power of ten and then find the ratio.
Park Crest Middle School has about 400 8th graders. We can round this number to 10³ or 1000, which is the nearest power of ten. The state has 806,240 8th graders, which we can approximate to 8x10⁵ (800,000) as the nearest power of ten. Now, to find how many times greater the state's population of 8th graders is, we divide the state's approximation by the school's approximation: State's approximation: 8x10⁵. Park Crest's approximation: 1x10³. Dividing the states by Park Crest's: (8x10⁵) / (1x10³) = 8x10². However, we want to find a number that's similar to the answer choices, which are in the form of 2x10ʹ, where n is an exponent. Since 8x10² is the same as 2x2x2x10², and 2³ equals 8, we can rewrite this as 2x10³. Therefore, the state's population of 8th graders is approximately 2000 times greater than that of Park Crest Middle School, which corresponds to answer choice (D) 2x10³.