What is 36 divided by 396?

Question

Isaiah Anthony · Accepted Answer

# 0.9090909...# going on for ever

Written mathematically as #0.90bar(90)# #color(blue)("Introduction to a very different approach")# #color(purple)("They are expecting you to do long division")# In this question we are dividing a lesser number by a greater number. Let me show you a trick. Consider the example: #3-:6 ->3/6 # This is smaller divided by larger We know that this is #(3-:3)/(6-:3)=1/2# .......................................................................... Suppose I turn this upside down then I have #6/3=2# I now have larger divide by smaller. It is perfectly correct to write #2" as "2/1# and if I turn #2/1# upside down I get #1/2# which is the correct answer for #3/6# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Answering the question")# Given:#" "36-:396 ->36/396# #color(red)("Invert this (turn upside down) and then do the division")# #color(green)("Write as "396/36) larr" deliberate act"# #"Starting point "->396# #color(magenta)(11)xx36 ->" "ul(396) larr" subtract"# #" "00# So #396-:36=11/1# #color(red)("Turn this answer upside down to answer the question")# This means that #36-:396 ->36/396 = 1/11# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Footnote")# By calculator: #1/11= 0.9090909...# going on for ever Written mathematically as #0.90bar(90)# If no one demonstrates long division I will return to this question.

Eva Abramson · Answer

#color(red)("Note that the question does not specify the method of division")#

Long division method.

#0.09bar(09)#

#0.09# to 2 decimal places

write as: # 396color(white)(.)bar(|color(red)(36))# ............................................. #36" less than "396# so write as: #" "0.# # 396color(white)(.)bar(|360)# ........................................................ #360" less than "396# so write as: #" "0.0# # 396color(white)(.)bar(|3600)# #3600" greater then "396# so we can do the division ..................................................... #" "color(purple)(0.09)# #" " 396color(white)(.)bar(|3600)# #9xx396 ->ul( 3564) larr" subtract"# #" "color(red)(36)# The #color(red)(36)# is a repeat of the starting point so this means that we will have a never ending repeat of #09# giving: #" "color(green)(ul(bar(|color(white)(2/2)color(purple)(0.09)color(white)(.)09090909..... color(white)(2/2)|)))# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(white)(.)# #color(blue)("Footnote")# This is how the real procedure ought to appear: #" "color(purple)(0.09)# # " "396color(white)(.)bar(|color(red)(36. color(white)() 00))# #" "ul(35color(white)(,)64) - # #" "36# ............................................................................................................ Note that some people much prefer the subtract sign to be to the left of 3564. So in that case it would look like. #" "color(purple)(0.09)# # " "396color(white)(.)bar(|color(red)(36. color(white)() 00))# #" "-ul(35color(white)(,)64) larr" alternative format"# #" "36# #color(brown)("Its position is a matter of current preferences. This changes over time")# If you go back far enough, you'll reach the period when I was a student, at which point the subtract was moved to the right. Back then, it was unquestionably: #" "color(purple)(0.09)# # " "396color(white)(.)bar(|color(red)(36. color(white)() 00))# #" "ul(35color(white)(,)64) - # #" "36#

Nathan Axel · Answer

undefined 36 divided by 396 equals 0.09090909090909091 or approximately 0.09 when rounded to two decimal places.