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Here's a boring, unshmoopy question you'll find on an exam somewhere in life...

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The decimal 0.000035 can be written in scientific notation as... what?

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Here are the potential answers...

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OK, so what's this question really asking?

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Well, it's all about how you simplify writing a realllllly small number.

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Just as when we raise 10 to a positive number it gets big fast...

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...the opposite happens when we raise it to a NEGATIVE number.

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We know that the standard form of writing in scientific notation is a single digit integer

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followed by a decimal and then a bunch of numbers...

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...so then the whole thing is raised to some power, either positive or negative,

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depending on if we want to move the decimal to the left or right.

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And technically the power is 0 if we just want the integer.

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So the first part of the problem needs us to get to a 3.5.

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Let's figure out how to get there before we do anything else.

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Well, we start with 0.000035.

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The decimal has to get from here. To here. No tolls.

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So we move it to the RIGHT -- 1 2 3 4 and 5 places.

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We moved it 5 to the right so we have to now "account" for that move by putting up

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the power which is -- yep -- negative 5.

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If we ever forget whether the power should be positive or negative depending on if whether

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move it left or right... ...we can just remember that if the power

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is positive, the actual number is going to be greater than 10...

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...and if the power is negative, the actual number will be less than 10.

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And we write it like this: 3.5 × 10 to the -5

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The answer is A.

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Note how close D was those... those test-making

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buggers are always trying to trip us up...

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so let's not forget the negative sign.

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