Question

How do you express 8,400,000 in scientific notation?

Answer 1

`8.4 xx 10^6`

Explanation:

Expressing a number in scientific notation means you will adjust the given number to result a more compact form of the number that may include rounding it off to match the precision of other numbers given.

Scientific notation is a compact way of writing numbers to reduce complicated computations using very large or very small numbers and to reduce errors.

In our example: `8,400,000 = 8.4 xx 10^6` in scientific notation.

To get this result we divided the given larger number repeatedly by 10, dropping a zero each time. While we did that, we added another `1` to the exponent of the `10` multiplier that is at the end of every number in scientific notation. It looks like this:

`8,400,000 = 8400000 xx 10^0` because we know `10^0 = 1`
`8,400,000 = 840000 xx 10^1` drop one `0` and exponent is `1`.
`8,400,000 = 84000 xx 10^2` drop two `0` and exponent is `2`.
`8,400,000 = 8400 xx 10^3` drop three `0` and exponent is `3`.
`8,400,000 = 840 xx 10^4` drop four `0` and exponent is `4`.
`8,400,000 = 84 xx 10^5` drop five `0` and exponent is `5`.

Having run out of zeros, we could stop here and not be numerically incorrect, but there is a definition of scientific notation called "normalized" that requires the first digit to reside between `0` and `9`.

So to become normalized, we must divide our number again by `10` so the first digit becomes `8`.
Remember to add to the exponent.

Then: `8,400,000 = 8.4 xx 10 ^6`

If you understand that method the easy way follows:

Place a dot (decimal point) at the right hand side of the original number of `8400000`. Notice we removed the commas.

Now move the decimal point to the left counting each time you pass a digit `8.4.0.0.0.0.0.`

If you count each `move` correctly you should reach `6` when you land between `8` and `4`.

Then: `8,400,000 = 8.4 xx 10 ^6`