Question

How do we write `50000` in scientific notation?

Answer 1

`50000=5xx10^4`

Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of `10`.

Note that moving decimal `p` digits to right is equivalent to multiplying by `10^p` and moving decimal `q` digits to left is equivalent to dividing by `10^q`.

Hence, we should either divide the number by `10^p` i.e. multiply by `10^(-p)` (if moving decimal to right) or multiply the number by `10^q` (if moving decimal to left).

In other words, it is written as `axx10^n`, where `1<=a<10` and `n` is an integer.

To write `50000` in scientific notation, we will have to move the decimal point four points to left, which literally means dividing by `10^4`.

Hence in scientific notation `50000=5xx10^4` (note that as we have moved decimal four points to left and thus divided by `10^4`, we are multiplying by `10^4` to compensate.

Answer 2

`5.0xx10^4`

Explanation:

Built in stages so that you can see what is happening

`50,000 ->5000xx10`

`50,000->500xx10xx10`

`50,000->50xx10xx10xx10`

`50,000->5xx10xx10xx10xx10`

Thus: `50,000 -=5.0xx10^4`