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OpenStudy (rainbow_rocks03):
OpenStudy (thetoetoejam):
1: C
2: B
3: B
OpenStudy (rainbow_rocks03):
plz explain?
OpenStudy (thetoetoejam):
No screw u
OpenStudy (thetoetoejam):
just convert them back to standard notation then mutiply, then convert back to scientific
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OpenStudy (rainbow_rocks03):
whats ur problem, ur supposed to explain not just give the answers
OpenStudy (rainbow_rocks03):
@jim_thompson5910 @jabez177
jimthompson5910 (jim_thompson5910):
@rainbow_rocks03 first you would multiply the base numbers 5.1 and 3.2
what do you get when you do this?
OpenStudy (rainbow_rocks03):
you get 16.32
jimthompson5910 (jim_thompson5910):
yes
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jimthompson5910 (jim_thompson5910):
then you add the exponents 3+3 = 6
jimthompson5910 (jim_thompson5910):
so \[\Large \left(5.1 \times 10^{3}\right)\times\left(3.2 \times 10^{3}\right) = 16.32 \times 10^{6}\]
but this is not the final answer. There's a bit more work needed to be done
jimthompson5910 (jim_thompson5910):
Recall that scientific notation must have the base be a number x such that \(\Large 1 \le x < 10\)
OpenStudy (rainbow_rocks03):
5?
OpenStudy (rainbow_rocks03):
im not sure
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jimthompson5910 (jim_thompson5910):
is 16.32 between 1 and 10? the answer is no
so we must convert 16.32 into scientific notation
jimthompson5910 (jim_thompson5910):
how can we do this?
OpenStudy (rainbow_rocks03):
idk
jimthompson5910 (jim_thompson5910):
we can move the decimal point 1 spot to the left to go from 16.32 to 1.632
to move the decimal point back, we move the decimal 1 spot to the right
the `move the decimal 1 spot to the right` is the same as multiplying by 10 = 10^1
which is why
\[\Large 16.32 = 1.632 \times 10^{1}\]
do you agree?
OpenStudy (rainbow_rocks03):
um, yes
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jimthompson5910 (jim_thompson5910):
So replace the `16.32` with `1.632 x 10^1` to go from this
\[\Large 16.32 \times 10^{6}\]
to this
\[\Large 1.632 \times 10^{1} \times 10^{6}\]
with me so far?