Given a computer with only

$5$

$$decimal digits of precision, find the largest open

interval about

$$

$=$

$1$

$6$

$$so that all real numbers

$$

$$from the interval are rounded to

$$

$$

$($

$$

$)$

$=$

$1$

$6$

$$That is

$,$

$$find the smallest value of a and the largest value of

$$

$$so that

any number

$$

$$from

$($

$$

$,$

$$

$)$

$$is rounded to the floating point number

$$

$$

$($

$$

$)$

$=$

$1$

$6$

$,$

$$i

$.$

e

$.$

$,$

$$

$$

$($

$$

$)$

$=$

$1$

$6$

$.$

$$Note: this is not a MATLAB computational problem, it must be

sorted out using the definitions of floating point numbers.