In this video we're gonna practice converting from standard notation to
scientific notation and vice-versa using three examples. So what is standard and
scientific notation? Standard notation is basically how we normally write out our
numbers like 0.001 for 2 for small numbers and 9715000 that's a large number.
Scientific notation on the other hand, it's written with only one digit in
front of the decimal point followed by the rest of the digits and then it's
accompanied with an exponent like this. Negative exponent indicates a small
number which is less than 1 and positive exponent represents a large number which
is greater than 1. Let's look at our first example. We need to find the volume
of the box so we multiply the three values and we get 0.000675 meter cube.
This is in standard notation. Now we need to convert
that to scientific notation, so to do that we need to move the decimal place
to the right four steps until we reach past 6. The reason we stopped at 6 is
because scientific notation requires one digit before the decimal place and has
to run from 1 to 9 since we move to the right.
We'll write the exponent with a negative 4 value. Final answer is 6.75
times 10 to the power of negative 4 meter cube. Moving on to our second
example, this is the opposite to the first question. Here we need to convert
from scientific notation to standard notation, so we write out 5.29177 times
10 to the power of negative 11. Moving on to our second example this is the
opposite of the first question here we need to convert from scientific notation
to standard notation so we write out 5.29177 times 10 to the power of
negative 11 as you can see it has a negative exponent value so that means is
a very small number far smaller than 1 so we'll need to move the decimal point
all the way to the left 11 times like this. It's 11 times because we have
the exponent negative 11. It's to the left because it's a negative exponent.
Let me fill in with zeros to make it clearer. There we go, so the final answer
is zero point ten zeroes five to nine one seven seven meter. Okay,
third and final question. We are given the distance in standard notation and we
need to convert that into scientific notation. Since this number is large that
means we'll end up with positive exponent value so we write out the
number that's given. Place in the decimal at the end, then we move the decimal to
the left until there's only one digit in front of the decimal point like this.
That gives us two point five two zero eight eight times 10 to the power of
five. The exponent is positive 5 because we move the decimal to the left five
times. Also because it's a larger number than one, the exponent value should be positive.
To recap, when going from standard to scientific notation for
large numbers we move the decimal to the left, we count the number of places that
we move and then we write that number in positive exponent. For smaller number we
move the decimal to the right count the number of places move and we write that
number in negative exponent. To convert from scientific to standard notation we
simply work backwards.
I hope this video helped you out somehow. Do subscribe and thanks for watching.
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