Chemistry: Significant Digits: Asking this question again ?

Question

(1.31 x 10^5) + (4.2 x 10^4)

i know that you have to change the exponents, so it becomes

(13.1 x 10^4) + (4.2 x 10^4)

and the answer is 17.3 x 10^4

but my book says the answer is 1.73 x 10^5 but that doesnt make sense because the number with least number of decimal places is in the tenth place not the hundredth!

Should i ignore the rules for finding how many significatn figures there are when adding?????????????

Answer 1

You are correct--when adding you want to maintain the same decimal place as the number with the least number of digits after the decimal.

However, 17.3 x 10^4 is not correctly written in scientific notation.

It is properly written as 1.73 x 10^5

In scientific notation, you should never have more than one digit in front of the decimal place in your final answer.

EDIT (in response to your additional details): No, the answer is still 1.73 x 10^5.  Here is why:

While performing your calculations you focus on the significant figures.  13.1 + 4.2 = 17.3  This is correct.  But when you finalize your answer you don't need to remove any numbers.  You simply move the decimal place as appropriate... 1.73 x 10^5.

For instance, what if we did the math a little differently?  Suppose you added the same numbers as follows:

(1.31 x 10^5) + (0.42 x 10^5) =  (1.73 x 10^5)

Each of the numbers have two decimal places, which is appropriate math for significant figures.  Plus, we don't need to rearrange the number to put it in correct scientific notation, because it already is.