Please help me I don't understand what to do for this, as I haven't learned what to do if I need to find the average of something in Scientific Notation. I tried doing it using division, but I got 0.62 x 10^2, which isn't one of the choices. Could someone please explain to me how I do it?
In a recent year, the population of California was about 2.52 x 10^7 people. It's land area is about 4.95 x 10^5 km^2. What was the average number of people per square kilometer?
A. 0.62 x 10^5
B. 6.2 x 10^1
C. 0.62 x 10^14
D. 6.2 x 10^9
Scientific notation always leaves one number to the left of the decimal
.62 x 10 ^2
move the decimal point 1 place to the right to get 6.2 and now the exponent becomes 1.
To find the average number of people per square kilometer, you need to divide the population by the land area.
First, let's write the given numbers in standard notation for easier calculation:
Population = 2.52 x 10^7 (as 2.52 multiplied by 10 raised to the power of 7)
Land area = 4.95 x 10^5 (as 4.95 multiplied by 10 raised to the power of 5)
To divide numbers in scientific notation, follow these steps:
1. Divide the coefficient (the numbers in front of the power of 10) by the coefficient.
2.52 ÷ 4.95 = 0.5090909...
2. Subtract the exponent of the denominator from the exponent of the numerator.
10^7 ÷ 10^5 = 10^(7-5) = 10^2
Putting it all together, we have:
0.5090909... x 10^2
Now, let's rewrite 0.5090909... in standard notation:
0.5090909... = 5.090909...
Therefore, the average number of people per square kilometer is approximately 5.09 x 10^2.
Comparing this result to the answer choices, we can see that none of the given options match 5.09 x 10^2 exactly. It seems there might be an error in one of the answer choices or in the original question. I would suggest double-checking the options or seeking clarification from the source of the question.