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) .
