How do you simplify #(0.4 times 10^-6)(0.7 times 10^-2)# and write the answer in scientific notation?

1 Answer
Jul 3, 2016

#(0.4xx10^(-6))(0.7xx10^-2)=2.8xx10^(-9)#

Explanation:

#(0.4xx10^(-6))(0.7xx10^-2)#

= #0.4xx10^(-6)xx0.7xx10^-2#

= #0.4xx0.7xx10^(-6)xx10^-2#

= #4/10xx7/10xx10^((-6)+(-2))#

= #28/100xx10^(-8)#

= #0.28xx10^(-8)#

Now to right the result in scientific notation, we need to shift decimal in #0.28#, one point to right (to make only one digit to left of decimal point), i.e. multiply by #10# and hence we should also multiply it by #10^(-1)#.

Hence #(0.4xx10^(-6))(0.7xx10^-2)=2.8xx10^(-1)xx10^(-8)=2.8xx10^(-9)#