Question

could you please explain operations with scientific notation using this example. 5 × 10³ + 4.3 × 10⁴ i dont understand how to solve it all . if you explain each step that would be great.

Answer 1

Explanation:

The scientific notation:

$a\times10^k$

where

$1\leq a$ and k is integer.

We have the example:

$(5\times10^3)+(4.3\times10^4)$

You can write the numbers in a "normal" form:

$5\times10^3=5\times1000=5000\\\\4.3\times10^4=4.3\times10000=43000$

Make the sum:

$5000+43000=48000$

And next write it in the scientific notation:

$48000=4\underbrace{8000}_{\leftarrow4}=4.8000\times10000=4.8\times10^4$

Other method:

You can add numbers in scientific notation if the power of tens in both number is the same.

Therefore you must convert the first number:

$5\times10^3=0.5\times10\times10^3=0.5\times10^4$

Now, you can make the sum:

$(5\times10^3)+(4.3\times10^4)=0.5\times10^4+4.3\times10^4=(0.5+4.3)\times10^4=4.8\times10^4$