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

2 Answers
Jan 9, 2018

1.054*10^-2

Explanation:

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

Jan 9, 2018

1.054 xx10^-2

Explanation:

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