Question

How do you write 540 in scientific notation?

Answer 1

`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`.