WEBVTT
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This is Giancoli Answers
with Mr. Dychko.
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For powers of 10 notation or also
called scientific notation,
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you need to have a single digit
to the left of the decimal
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and then you multiply by 10 to the power of
whatever it takes to make the
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quantity that you actually want.
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So in the first case here,
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multiplying by 10 to the power of something
is a bit silly because there's nothing to do;
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it already has one digit to
the left of the decimal.
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But if we have to multiply by times
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10 to the power something, we'll go
10 to the power of zero
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because that is the number 1 and so
it doesn't change it at all.
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In part (b), we have 21.8
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and the reason I know that it's
10 to the power of 1
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is because well first I ask
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what should I do to this number
in order to make only a single
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digit to the left of the decimal
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and I mean which power of 10 should I
multiply or divide by
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and in this case, I'd have to divide by
10 to the power of 1
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in order to make 21.8 into 2.18
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and then you have to compensate for that
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by multiplying by the same thing times
10 to the power of 1
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because in fact, you are multiplying by
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the number 1 although it doesn't look like it
but it's 10 to the 1 over 10 to the 1
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and it's always that way for
all of these conversionsâ€”
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you are multiplying by 1 in the senseâ€”
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because you are not actually allowed
to change the quantity;
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you wanna have the same value,
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you just want it represented differently.
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So first step is to figure out what to do
to make this given number
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have one digit to the left of the decimal
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and then in this case, you divide by
10 to the power of 1
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and then what needs to be done
to undo that change
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and so we multiply by 10 to the power of 1
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and this is what we'll write here.
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So we have 2.18 times 10 to the 1
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is the same quantity as what
we started with 21.8.
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For 0.0068 to get this decimal place
three places to the right,
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you multiply by 10 to the power of 3.
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Now we have to undo that though
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and then divide by 10 to
the power of 3 as well
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but dividing by 10 to the power
of 3 is the same as
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multiplying by 10 to the negative 3
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so that kind of explains what this is about.
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So anytime you divide by 10 to the power of
something, it's the same as multiplying by
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10 to the negative of that;
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that negative exponent is also thought of as
reciprocal or dividing by.
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And then same kinda thing going
forward here, we have
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328.65 divided by 10 to the power of 2
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to move this decimal place
to the left twice
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and then undo that change by multiplying by
10 to the power of 2
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and our answer will be 3.2865
times 10 to the 2.
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And then for this one, you have to
multiply by 10 to the power of 1
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and then what do we have to undo
that change
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divide by 10 to the 1 and whatever
it is that you have to
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do to undo the initial change
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is what gets put over here and when
you are dividing by
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10 to the power of something, it's times
10 to the negative of that exponent.
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And 444 is
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decimal place goes twice to the left
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so that means divide by 10 to the 2
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and to undo that change,
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you multiply by 10 to the 2 and this
is what ends up going here;
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4.44 times 10 to the 2 there.