You didn't give any problems,
so I'll make some up. I hope they are
like the ones you were asked to solve.

All rational numbers expressed
as decimals will either terminate
or repeat a block of digits
forever.  That's because in long
division all the remainders will
always be less than the divisor,
so sooner or later the remainder
will either be 0 or will be the
repeat of a remainder obtained
earlier.

write the decimal expansions for these 
rational numbers. tell whether the 
expansions are terminating or repeating. 

#1.   9/32

Use long division:

    .28125 
32)9.00000
   6 4
   2 60
   2 56
      40
      32
       80
       64
       160
       160
         0

Terminating because the division 
eventually has 0 remainder

#2. 15/22

Again use long division:

     .6818 
22)15.0000 
   13 2
    1 80
    1 76
       40
       22
       18 

This is a repeating decimal because the same 
non-zero remainder 18 occurred twice in the 
long division. These two 18's are indicated in 
red above.


--------------------------------------------

Find the rational number equivalents for these 
decimal expansions. tell whether they are 
rational or irrational

#3.   .185185185185···

Let N = .185185185185···
There are 3 digits in the repeating block
"185", so multiply by 103 or
1000

1000N = 185.185185185···

Now place the first equation underneath
and subtract the two equations

1000N = 185.185185185···
    N =    .185185185185···
 999N = 185.000000000
 999N = 185
    N = 185/999
that reduces to
    N = 5/27

This is RATIOnal because it is the
RATIO of two integers

#2.  2.9373737837···

Let N = 2.937373737··· 

There are 2 digits in the repeating block
"37", so multiply by 102 or
100

100N = 293.737373737···

Now place the first equation underneath
and subtract the two equations

100N = 293.737373737···
   N =   2.93737373737···
 99N = 290.800000000···
 99N = 290.8
Clear of decimals by multiplying thru
by 10

990N = 2908
   N = 2908/990
that reduces to
    N = 1454/495

This is RATIOnal because it is the
RATIO of two integers
  
#3.  .72772277722277772222···

This is IRRATIONAL because  
there is no block of repeating
digits.

--------------------------------------------

simplify the following 
radicals. 

#4.  

#5. 

Edwin