How do you write 52/3 as a percent?

#(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:

• Move the decimal point 2 places to the right

• Add the % sign

# 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#