How do you write #0.125# in scientific notation?

1 Answer
Aug 19, 2016

Answer:

#0.125 = color(green)(1.25xx10^(-1) ("normalized")#

Explanation:

Numbers in scientific notation are written as the product of two components:
#color(white)("XXX")"the "color(red)("mantissa")#
and
#color(white)("XXX")"10 to some integer "color(blue)("exponent")#

In #color(green)("normalized")# form, the #color(red)("mantissa")# (unless zero) is written as a decimal fraction with exactly one non-zero digit before the decimal point.

Using a #color(red)("mantissa")# of #color(red)(1.25)#
with an #color(blue)("exponent")# of #color(blue)(2)#: #color(red)(1.25)xx10^color(blue)(2) = color(brown)125#
with an #color(blue)("exponent")# of #color(blue)(1)#: #color(red)(1.25)xx10^color(blue)(1) = color(brown)12.5#
with an #color(blue)("exponent")# of #color(blue)(0)#: #color(red)(1.25)xx10^color(blue)(0) = color(brown)1.25#
with an #color(blue)("exponent")# of #color(blue)(-1)#: #color(red)(1.25)xx10^color(blue)(-1) = color(brown)0.125# [#color(green)("the value we wanted")#]