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Very large or very small numbers are best input with exponential notation. For instance, the number 8,000,000 (eight million) is equal to 8×106 . In this course, you can enter that as either 8 * 10 ^ 6 or as 8e6 in these problems. Try out exponential notation in the question below.

One light year is equal to 9,460,730,472,580.8 kilometers. Enter this number below in exponential notation. The tolerance on this question is 5%.

________km

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Answer:

[tex]9*10^{12}km[/tex]

Step-by-step explanation:

[tex]9,460,730,472,580.8 km[/tex]

First, we can work out 5% of our number, by multiplying it by 0.05

[tex]9,460,730,472,580.8 * 0.05 = 473,036,523,629[/tex]

Now, if we add and subtract our 5% calculated from our original number, we can work out the minimum and maximum value that our final answer can be in the range of.

[tex]9,460,730,472,580.8 + 473,036,523,629 = 9.933767*10^{12}\\9,460,730,472,580.8 - 473,036,523,629 =8.98769395*10^{12}[/tex]

We can see that [tex]9*10^{12}[/tex] is in the range of valid answers, as:

[tex]8.9*10^{12} \leq 9*10^{12} \leq 9.9 * 10^{12}[/tex]

So, our final answer is:

[tex]9*10^{12}km[/tex]

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