Scientific notation

Question

Suppose a geographic area of California in the USA are 1.637 times 10 to the 5th power and 3.794 times 10 to the sixth power square miles, respectively. California population is approximately 3.804 times 10 to the 7th power, at the population and were proportional to area, what would be the US population.

Answer 1

The problem used the phrase "population ... proportional to the area."  Supposing that proportion (or ratio) is constant, then we may set them equal:

     (pop of CA) / (area of CA) = (pop of US) / (area of US)

 

Let x = pop of US

 

    (3.804 * 10^7) / (1.637 * 10^5) = x / (3.794 * 10^6)

 

Now, you may either divide powers of 10 (remember, subtract the exponents) before or after cross-multiplying:

    (3.804 * 10^7) * (3.794 * 10^6) = (1.637 * 10^5) * x

      8.816 * 10^8 = x

Answer 2

I think you need to express the terms of the question more clearly.

 

Are you saying: the geographic area of CA= 1.637 *10^5 mi^2

geographic area of USA= 3.794 * 10^6 mi^2

 

and that the population is directly proportional to geographic area?

 

Those numbers feel wrong though if we're including Alaska - that does skew things from an area perspective. I'm assuming this is just a problem & not reality since geographical area is definitely not on a 1:1 basis with the population size.

 

essentially it would be a fraction with

1.637/37.94 being the fraction of CA has of both geography and population of the US. so just solve for that using the population number.

 

Basically multiply that CA population amount (3.804 * 10^7) * 37.94 and divide by 1.637

8.816 * 10^8