Express nine times 10 to the sixth
power times 11 times 10 to the fourth power in scientific notation.
To solve this problem, I’m gonna
use the commutative property of multiplication. The commutative property of
multiplication tells me that I can multiply numbers in any order to produce the same
outcome. So let’s re-group this
Let’s group the nine times 11
together and then group 10 to the sixth power times 10 to the fourth power. Nine times 11 is 99. 10 to the sixth power times 10 to
the fourth power equals 10 to the six plus four. We add those exponents
together. So this number is 99 times 10 to
the tenth power. Unfortunately, this is not
scientific notation. It looks like it’s almost in
scientific notation, 𝑎 times 10 to the 𝑏.
For scientific notation, we need
our 𝑎 to be greater than or equal to one but less than 10. Our 99 is larger than 10, so it
doesn’t qualify. So I’m gonna add a decimal at the
end of the 99 and I’ll move the decimal one place to the left.
Since I moved the decimal one point
to the left, I’ll have 99 equal to nine point nine times 10 to the first power. We can multiply that by 10 to the
tenth power. We add the one and the 10 to give
us nine and nine tenths times 10 to the 11th power. This is the product of the above
multiplication problem in scientific notation, nine and nine tenths times 10 to the