How do you simplify #(2.68×10^-5)×(4.40×10^-8) #?

1 Answer
George C.
Jul 22, 2015

#(2.68 xx 10^(-5)) xx (4.40 xx 10^(-8))#

#=(2.68 xx 4.40) xx (10^(-5) xx 10^(-8))#

#=11.792 xx 10^(-13)#

#=1.1792 xx 10^(-12)#

Explanation:

Note that #a^b * a^c = a^(b+c)#

So #10^(-5) xx 10^(-8) = 10^(-5+(-8)) = 10^(-13)#

When we multiply the mantissas #2.68 xx 4.40# the result is greater than #10#, so we divide it by #10# and adjust the exponent accordingly to give the result in scientific notation.

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