There are a number of ways to implement the functionality described in this problem and it can be done using only the language features described in lecture. Figuring out the implementation is a large part of the challenge. Another part will be figuring out how to give Gradescope exactly what it wants.

Often times two seemingly equivalent calculations will arrive at slightly different floating point results due to rounding errors inherent in the representation of these numbers in the computer.

$```$

$>>>$ print$("$Weight on moon:", $100/6)$

Weight on moon: $16\mathrm{.}666666666666668$

$``$ print$("$Weight on moon:", $100*(1/6))$

Weight on moon: $16\mathrm{.}666666666666664$

$```$

To circumvent this issue some sort of approximate equality is almost always used when comparing two floating point numbers. In this problem you will explore an implementation of approximate equality.

Two numbers are the same to $2$ decimal places if the absolute value of their difference is less than $0\mathrm{.}01.$ They are the same to $4$ decimal places if the absolute value of their difference is less than $0\mathrm{.}0001,$ and so on$.$

You will write a program that takes two floating point numbers as input. If the numbers are identical then it will print "Those numbers are identical" as illustrated below.

Enter a number: $3\mathrm{.}14$

Enter a number: $3\mathrm{.}14$

Those numbers are identical

If the numbers are the same to $2-9$ decimal places, the program will print "Those numbers are the same to N decimal places" $($where N is a number from $2$ through $9)$ as illustrated below.

Enter a number:$3\mathrm{.}1415926$

Enter a number: $3\mathrm{.}1415928$

Those numbers are the same to $6$ decimal places

If the numbers are the same to more than $9$ decimal places the program will print "Those numbers are nearly identical" as illustrated below.

Enter a number: $16\mathrm{.}666666666666668$

Enter a number: $16\mathrm{.}666666666666664$

Those numbers are nearly identical

If none of the previous categories apply because the numbers are the same to $1$ or fewer decimal places, the program will print "Those numbers are different" as illustrated below.

Enter a number: $3\mathrm{.}14$

Enter a number:$3$

Those numbers are different

Save this and submit your completed program to gradescope as approx.py