Vegita wrote:
Hey there guys,
Could anyone please explain me what the phrase "the nearest power of 10" means?
The “
Power of 10” is any of the integer exponents of the number 10. In other words, the number of 10s indicated by the exponent, multiplied together.
For example: 10 to the 3rd power is 10 x 10 X 10 = 1,000.
If the exponent is greater than zero, written in long form, a power of 10 is the number 1 followed by
n zeros.
N being the exponent.
Example: \(10^8\) equals 1 with 8 zeros behind it --> 100,000,000
If the exponent is less than zero, written out, the power of 10 is 1 with
n places
after the decimal point.
N again being the exponent.
Example: \(10^{-3}\) is 1 with three places after the decimal point --> 0.001
In this particular problem, they are asking you to find the answer “to the nearest power of ten” because all of the answer choices are listed in powers of ten. By looking at the graph, we see that in year 1, the cost of fertilizer (per 10 kg of apples) is 0.05 and in year 5, the cost is 0.005. To calculate the actual average, first get the total difference
0.05 – 0.005 = 0.045
And divide it by the number of years
0.045 / 5 = 0.009
So, 0.009 is the
true average, but the question asks you to find the average
to the nearest power of 10. 0.009 is not a power of 10, so we need to round up a bit. Hence, 0.01 is the answer.
That’s the very long answer. The short answer is, because this is an integrated reasoning question, they probably just want to make sure you can read a graph correctly. The trick is not to focus on the actual average (doing the exact math to calculate 0.009), but to look at the graph and estimate by about how much the cost is decreasing per year. The cost of fertilizer per 10 kg of apples sold is listed on the right-hand side of the graph. Over 5 years, each year, the cost seems to go down by about 0.01 dollars.