# What to do if a number becomes bigger than 10 on scientific notation when performing arithmetics with it?

For example, I was adding (9.99 x 104)+ (9.99 x 105).

I raised the first number's exponent from 4 to 5 by dividing it by 10 once more, thus getting 0.999 and the 105 exponent as a way to reverse it (that's how I see scientific notation, you either divide or multiply by ten successive times and then you have the reverse process as scientific notation, so if I get a positive exponent, it reverts a corresponding exponentiation which has a negative exponent, and the converse is also true).

The problem is that after that, when adding 9.99 with .999 I get 10.989 and my final number is 10.989 x 105, which is not a valid number in scientific notation as far as I know.

PS: sorry for my explanation, it feels a bit confused even to me, but that's the best I could conceive as an explanation to the issue I have.

TL;DR (9.99 x 104)+ (9.99 x 105) = 10.989 x 105, how the hell do I solve it?

• $10\times 10^5 = 1\times 10^6$. – Ted Shifrin Nov 29 '18 at 23:30
• Note that $10.989 = 1.0989\times 10^1$ and so $10.989\times 10^5 = (1.0989\times 10^1)\times 10^5 = 1.0989\times (10^1\times 10^5)=\dots$ – JMoravitz Nov 29 '18 at 23:30

Remember that scientific notation is just a way to write a number. Its not a special code outside of other math. It's just like we identify the number $$20$$ and the number $$4\times 5$$ since they are equal.
So in this case, we want to write $$9.99\times 10^4+9.99\times 10^5$$ in scientific notation. We can use the fact that $$9.99\times 10^5=9.99\times 10\times 10^4=99.9\times 10^4$$ along with the fact that $$ax+bx=(a+b)x$$ to see $$9.99\times 10^4+9.99\times 10^5=109.89\times 10^4.$$ Now $$109.89=1.0989\times 10^2$$, so we have $$109.89\times 10^4=1.0989\times 10^2\times 10^4=1.0989\times 10^6.$$