#(52)/(3)# is way more than #1# (way more than #100%#)
#100%# would be #(3)/(3)#
#(3)/(3) =1= 100%#
#(60)/(3)# is #20# times greater than #(3)/(3)#, and #(53)/(3)# is almost as much as #(60)/(3)#
So you can expect that the answer will be almost as large as #(60)/(3)#
which is #20# times as much as #100%#, which is
#20 xx 100%#, which is #2000%#
So you can expect that the correct answer will be
"#"almost as much as"# #2000%#"
#color(white)(mmmmm.)#―――――――
One way to write #(52)/(3)# as a percent is to first turn the fraction into a decimal.
#(52)/(3)# means #52-: 3#
#color(white)(....)#1 7 #.# 3 3
#color(white)(...)#―――――
#3 ) 5 2 . 0 0#
#color(white)(m)#- 3
#color(white)(...)#―――
#color(white)(mn)#2 2
#color(white)(m)#- 2 1
#color(white)(....)#―――
#color(white)(mmn)#1 0
So as a decimal, #(52)/(3)# equals # 17.bar(3333#
#color(white)(mmmmm.)#―――――――
To turn a decimal into a percent:
# 17.bar(3333) = 1733.bar33%# #larr# answer
#color(white)(mmmmm.)#―――――――
Check
The answer of #1733%# matches the estimate of
" #"almost as much as"# #2000%#"
So it's probably right.
#Check# #color(lightgreen)sqrt#
