$2\mathrm{.}3\mathrm{.}1$: Normalized scientific notation.

Write the number in normalized scientific notation.

Use ${?}^{{?}^{{?}^{?}}}$ for exponents. Ex: ${10}^{{?}^{{?}^{?}}}4$ for ${10}^4.$

$171\mathrm{.}975=Ex$: $1\mathrm{.}23{10}^{{?}^{{?}^{?}}}3$

MATLAB uses the IEEE $754$ standard for floating$-$point representation, having the form $1.f{2}^{\text{e}\text{x}\text{p}},$ where $f$ is the fraction par

mantissa, and exp is the exponent. The standard defines a $64-$bit floating$-$point representation known as double precision

$1$ bit $($bit $63)$ for the sign. $0$ indicates the number is positive. $1$ indicates the number is negative.

$11$ bits $($bits $62$ to $52)$ for the exponent.

$52$ bits $($bits $51$ to $0)$ for the fractional part of the mantissa; the whole part of the mantissa is always $1$ and thus is not

The default MATLAB floating$-$point representation is double precision.

The standard also defines a $32-$bit floating$-$point representation known as single precision, with $1$ bit for the sign, $8$ bits for th

and $23$ bits for the fractional part. The programmer can create a single precision number as follows: var $.$

precision number uses less space in memory, but has a smaller range compared to a double$-$precision number.

The following table shows the range for double precision and single precision floating$-$point variables along with the smallest

a number $($i$.$e$.,$ the smallest possible positive or negative numbers$)$