Addition/Subtraction and Multiplication/Division of Scientific notation

Question

How do we add/subtract, multiply/divide our scientific notations?

Here are examples:

$$4.53 \times 10^5 + 2.2 \times 10^6$$

$$(3.5 \times 10^2) \times (6.45 \times 10^10)$$

Answer 1

Simply use the properties of the operations in $\mathbb{Q}$, and remember the properties of the integer exponents of the same basis. So: $$ (3.5\times 10^2)(6.45 \times 10^{10})=(3.5 \times 6.45) (10^2\times10^{10}) $$ by commutativity and associativity, and $$ =22.575 \times 10^{2+10}=22.575 \times 10^{12}=2.2575\times 10 \times 10^{12}=2.2575\times 10^{13} $$

For $4.53 \times 10^5 +2.2\times 10^6$, first use distributivity so that :

$$ 4.53 \times 10^5 +2.2\times 10^6=(4.35+2.2\times 10)\times 10^5 $$

than.... can you do?