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

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#