Question

What is mantissa? Please

Answer 1

The mantissa is the part of a number written in scientific notation that shows the "pattern" of the number (as opposed to the scale of the number).

Explanation:

When a regular number is written in scientific notation, it is written with two significant components:
`color(white)("XXX")`the mantissa, and
`color(white)("XXX")`the exponent.

The exponent is always the number of times the mantissa pattern needs to be multiplied by `10` to obtain a value equal to the "regular number".

For example the regular number `52976` might be written in scientific notation as
`color(white)("XXX")color(red)(5.2976)xx10^color(blue)(4)`
or, (less common these days) as
`color(white)("XXX")color(red)(5.2976)Ecolor(blue)(+4)`
In either form the `color(red)("mantissa")` is `color(red)(5.2976)`

In standard scientific notation, the mantissa is always written with one non-zero digit to the left of the decimal point.
So, for example, while `color(red)(847.13)xx10^color(blue)(1)` is in scientific notation (with a mantissa of `847.13`) it is not in standard scientific notation which would be `color(red)(8.4713)xx10^color(blue)(3)`.

It should also be noted that for values with small magnitudes (absolute values less than 1), the exponent may be negative indicating the number of times the mantissa would need to be divided by `10` to get the "regular value".
For example `color(red)(2.914)xx10^(color(blue)(-5))` would be equivalent the the "regular value" `color(green)(0.00002914)`