# How do you calculate (1.025times10^4) + (9.814times10^5)?

Apr 28, 2017

$9.9165 \cdot {10}^{5}$

#### Explanation:

Here, you are taking two numbers that are in scientific notation and adding them.

color(white)(aaaaaaaaaaa)(1.025×10^4)+(9.814×10^5)

The thing to remember when adding in scientific notations is that you must have the base of 10 expressed with the same exponent.

So you $\textcolor{red}{\text{CANNOT}}$ add the two together and get something like this

color(white)(aaa)wrong->[(1.025×10^4)+(9.814×10^5) = 10.839 * 10^9]

$- - - - - - - - - - - - - - - - - - - - -$

To solve, you would have to change either the exponent in (1.025×10^4) to 10^5 or (9.814×10^5) to 10^4. We will do the former.

To change (1.025×10^4) in order to express the $\text{base 10}$ as ${10}^{5}$, then using our little mnemonic,

$\textcolor{w h i t e}{a a a a a a a a}$I $\textcolor{red}{\text{left it bigger}}$, but you're $\textcolor{b l u e}{\text{right, it's smaller}}$

you would move the decimal point to the $\textcolor{red}{\text{left}}$ of 1, moving it 1 time because to get from $4 \to 5$ you get $\textcolor{red}{\text{bigger}}$ in value so you move left.

color(white)(aaaaaaaa)(1.025×10^4)color(white)(aaaa)"becomes"color(white)(aaaa) (.1025*10^5)

(.1025×10^5)+(9.814×10^5) = 9.9165 * 10^5
Note: You do not do anything with the base ${10}^{5}$. You just have to express the scientific notations to have the same base and exponent in order to add at all