How do you write 540 in scientific notation?

1 Answer
Jul 27, 2015

Answer:

#540 = 5.4*10^2#

Explanation:

The purpose of scientific notation is to write very small or very large numbers in a shorter more comprehensible form.
For instance, US debt is now about $18 trillion. This huge number looks like
#18000000000000# (dollars)
Too many zeroes, is not it.

Say, you want to compare it with the distance from Earth to Sun, which is #150# million kilometers, that in standard units accepted by physicists - meters - looks like
#150000000000# (meters)
Also a lot of zeroes.

To easier see the magnitude of a number it is represented in scientific notation as a number from 1 to 10 multiplied by a number 10 in some power.
Thus,
#18000000000000 = 1.8*10^13#
#150000000000 = 1.5*10^11#

Now it's obvious that the first number more than in #100# times greater than the second because the front parts, called mantissa, (#1.8# in one case, #1.5# in another) are close to each other, while the powers of #10#, called exponent, are significantly different, one is #13#, while another is #11#, so the multiplier of #10# to some power is greater in the first case by #10^2#, that is the first number is greater than the second by at least a factor of #100#.