ShmoopTube

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Here's a shmoopy question for you...

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Melvin has been in prison for almost 3 years

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and, like many of his inmates, he marks his time on the wall of his cell.

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However, Melvin likes to mark every second that he's been

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incarcerated, rather than just every day.

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He has now been in jail for 86,310,000 seconds...

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and he feels like his routine is getting a little stale. Imagine that.

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He wants to write the number in scientific notation to... mix things up.

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How would he do that? And here are the potential answers...

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This question is testing one thing and one thing only...

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...did we show up for class the day our teacher taught us what scientific notation is.

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No way to brute force it... either we know it or we don't.

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If we make a mistake, it's gonna be because we messed up the zeros... where the decimal goes.

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So an easy way to check ourselves is to WRITE OUT THE PROBLEM with the decimal. Like this.

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Yes. The "point zero" at the end is important in this case.

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In scientific notation, the decimal point always ends up behind the first significant digit...

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...which in this case, is behind the 8.

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Now we just count the places between where

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the decimal exists and where it would have to go to sit next to the eight...

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...and we just count 1 2 3 4 5 6 and 7 places, moving it to the left.

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We moved seven places to the left, to the left... isn't there a Beyonce song like that?

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Anyway -- we move 7 places and you'll note that this corresponds beautifully to the way

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10 acts when we put it to a... higher power.

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That is, 10 squared is to the 2nd power has 2 zeroes; 10 cubed is to the 3rd power

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and has 3 zeroes... and so on.

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So it'd make sense that 10 to the 7th

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would give us a number with 7 integers before the decimal.

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When we are playing with this big honkin' multiplier,

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the numbers AFTER the decimal actually matter...

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...in real life, it'd be easy to just toss out everything after the decimal when the

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scale says you weigh 272.342981 pounds. Two seventy-two is big enough.

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But here, those numbers matter.

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With choice B, for example, we'd be off a bit.

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8.63 x 10 to the 7th would give us only 86,300,000 seconds...

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and Melvin already carved that number into the wall ages ago.

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Well, okay... ten seconds ago, but still... it isn't exact.

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So the answer is C... 8.631 × 10 to the 7th.

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