Question

How do you write `0.125` in scientific notation?

Answer 1

`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")`]