How do you write the answer in scientific notation given #(3.4times10^-1)(3.1times10^-2)#?

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Answer 1 · 2018-01-09T14:37:33

#1.054*10^-2#

Scientific notation is a notation which can be written as

#x * 10^n#

where #x in [1,10)# .

When multiplying, the first thing to do is to multiply the like terms.

#3.4*3.1=10.54#
#10^-1*10^-2=10^-3#

So the answer looks like it should be

#10.54*10^-3#

but it isn't, because #x# (as defined earlier), is not between 1 and 10. So we divide #x# by 10 and add one to that power to get the final answer:

#1.054*10^-2#

Answer 2 · 2018-01-09T15:37:32

#1.054 xx10^-2#

Consider the product: #" "3x^4 xx 5x^7#

In algebra we multiply the numbers:

#" "3 xx5 =15#

Then add the indices of bases that are the same:

#x^4 xx x^7 = x^(4+7) = x^11#

#3x^4 xx 5x^7 = 15x^11#

Scientific notation works in exactly the same way:

#(3.4 xx10^-1) xx (3.1 xx10^-2)#

Multiply the numbers:

#3.4 xx3.1 = 10.54#

Add the indices of bases that are the same:

#10^-1 xx 10^-2 = 10^(-1-2) = 10^(-3)#

#(3.4 xx10^-1) xx (3.1 xx10^-2) = 10.54 xx 10^-3#

However a value in scientific notation must only have one digit before the decimal point. it is written in the form:

#a xx 10^n," "# where #1<= a <10 and n in ZZ#

#10.54 xx 10^-3 = 1.054 xx10^-2#