Why are some numbers written in scientific notation?

Scientific notation makes it much easier to write numbers
that are very big or very small, and to work with them.

Examples:

Without scientific notation:
A particular band of gamma rays has a wavelength of
0.000000000002 meter.
How many of those gamma ray waves would fit parallel to a wave
of green light with wavelength of  0.0000005 meter ?

 0.0000005 meter divided by 0.000000000002 meter  =  ?

With scientific notation:
A certain band of gamma rays has a wavelength of  2 x 10⁻¹²  meter.
How many of those gamma ray waves would fit end-to-end, parallel to
a wave of green light with wavelength of  5 x 10⁻⁷ meter ?

         (5 x 10⁻⁷) / (2 x 10⁻¹²) = (5/2  x  10⁻⁷⁺¹²) = 2.5 x 10⁵ waves

Without scientific notation:
One astronomical unit ... the distance between the Earth and the sun ... is a distance of about  92,960,000 miles.
One light year ... the distance that light travels through vacuum in a year ... is a distance of about  5,879,000,000,000 miles.
How many Astronomical Units are equivalent to one light year ?

5,879,000,000,000 miles divided by 92,960,000 miles  =  ?

With scientific notation:
One astronomical unit ... the distance between the Earth
and the sun ... is about  9.296 x 10⁷ miles.
One light year ... the distance that light travels through vacuum
in a year ... is about  5.879 x 10¹² miles.
How many Astronomical Units are equivalent to one light year ?

5.879 x 10¹² / 9.296 x 10⁷ = 0.632 x 10¹²⁻⁷  =  6.32 x 10⁴

                                                                        or  63,200  (rounded) .