Order of operation with piping

My question is where does the piping operator of magrittr package %>% come in the order of operations?

I have a problem simmilar to the following:

set.seed(10)
df <- data.frame(a=rnorm(3),b=rnorm(3),c=rnorm(3))
df/rowSums(df)  %>%  round(.,3)

This results in the following non rounded figures:

           a        b         c
1 -0.0121966 0.119878 0.8922125

To get the rounded figures I need to put df/rowSums(df) between brackets.

I experimented with the +,-,*,/ and ^ and from the results I found the order of operation is as follow:

Exponents
Piping
Multiplication and division
Addition and subtraction

Is that right or there is something wrong with my understanding of the piping operator?

The help page you are looking for is ?Syntax. (Don't feel bad for not being able to find this, it took me about six guesses at search keywords.) I'm going to quote its entire operator precedence table here:

The following unary and binary operators are defined. They are listed in precedence groups, from highest to lowest.

   ‘:: :::’           access variables in a namespace              
   ‘$ @’              component / slot extraction                  
   ‘[ [[’             indexing                                     
   ‘^’                exponentiation (right to left)               
   ‘- +’              unary minus and plus                         
   ‘:’                sequence operator                            
   ‘%any%’            special operators (including ‘%%’ and ‘%/%’) 
   ‘* /’              multiply, divide                             
   ‘+ -’              (binary) add, subtract                       
   ‘< > <= >= == !=’  ordering and comparison                      
   ‘!’                negation                                     
   ‘&  &&’            and                                          
   ‘| ||’             or                                           
   ‘~’                as in formulae                               
   ‘-> ->>’           rightwards assignment                        
   ‘<- <<-’           assignment (right to left)                   
   ‘=’                assignment (right to left)                   
   ‘?’                help (unary and binary)

So magrittr's pipe operators, like all the operators of the form %whatever%, do indeed have precedence greater than multiply and divide but lower than exponentiation, and this is guaranteed by the language specification.

Personally, I don't see the value in these operators. Why not just write