awk not rounding with OFMT and $0 - awk

Question

I'm printing an array with 100 columns and I would like all columns to have 2 decimals. I would like to use print $0 and not have to individually specify the format for all columns.
OFMT does seen to work with $0:
echo '0.77767686 0.76555555 0.6667667 0.77878878' |awk '{CONVFMT="%.2g";OFMT="%.2g";print ($0+0);print ($0+0)"";print $0}'
Results:
0.78
0.78
0.77767686 0.76555555 0.6667667 0.77878878

Answer 1

Note that all input is treated as strings until implicitly converted by how it is used.
OFMT is used when strings are converted to numbers numbers are printed, e.g.:
<<< 0.77767686 awk '{ print 0+$0 }' OFMT='%.2g'
CONVFMT is used when numbers are explicitly converted to strings, e.g.:
<<< 0.77767686 awk '{ print "" 0+$0 }' CONVFMT='%.2g'
Output in both cases:
0.78
The latter converts $0 into a number and then concatenates it with the empty string.
To achieve this for every column I would suggest using a sensible setting of the input and output record separators:
<<< '0.77767686 0.76555555 0.6667667 0.77878878' \
awk '{ print 0+$0 RT }' CONVFMT='%.2g' RS='[ \t\n]+' ORS=''
Note the two conversions, first to a number with 0+$0 then back to a string by concatenating it with RT. RT will be set to the matched record separator. Note that this is GNU awk specific, for a more portable solution, use a loop, e.g.:
<<< '0.77767686 0.76555555 0.6667667 0.77878878' \
awk '{ for (i=1; i<=NF; i++) $i+=0 } 1' CONVFMT='%.2g'
Output in both cases:
0.78 0.77 0.67 0.78
Edit - Responding to #BeeOnRope
#BeeOnRope is correct, OFMT is used as the format specifier when the print-function calls sprintf(), while CONVFMT is used in other conversions. Here is an example that illustrates the difference:
<<< 0.77767686 awk '{ n=0+$1; s=""n; print n, s }' OFMT='%.2g' CONVFMT='%.3g'
Output:
0.78 0.778
Two relevant sections from the GNU awk manual:
https://www.gnu.org/software/gawk/manual/html_node/OFMT.html
https://www.gnu.org/software/gawk/manual/html_node/Strings-And-Numbers.html

Answer 2

Why don't you use a for loop?
echo '0.77767686 0.76555555 0.6667667 0.77878878' |awk '{ for (i=1; i<=NF; i++) printf "%.2f\n", $i }'
Results:
0.78
0.77
0.67
0.78

Answer 3

As others have mentioned you need to treat the field as a number to get a conversion. To combine some other ideas you can try:
awk '{ for (i=1; i<=NF; i++) $i += 0; print }'
That will convert every field to a number. You can just convert individual fields with $7 += 0 and so on. You could get fancier by using if (match($i, ...)) with some regexp to select only the numbers you want to convert.