What is the decimal equivalent of #16/3#?

1 Answer
Tony B
Jan 26, 2018

#16/3-=5.3bar3color(white)(..)# where #-=# means equivalent to

Explanation:

#color(blue)("There are some equivalents that are worth committing to memory.")#
#color(green)(1/10->0.1)#

#color(green)(2/10->1/5->0.2)#

#color(green)(3/10->0.3" and so on")#

#color(brown)( 1/2->0.5)#

#color(brown)(1/4->0.25)#

#color(brown)(1/3->0.3bar3" where the "bar3" means that the 3 repeats for ever")#
#color(brown)("So if we have "1/3->0.3bar3" then "2/3->0.6bar6)#

#color(brown)(1/8->0.125)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

#16/3 -> 3/3+3/3+3/3+3/3+3/3+1/3#

#16/3->ubrace(1color(white)(".")+color(white)(".")1color(white)(".")+color(white)(".")1color(white)(".")+color(white)(".")1color(white)(".")+color(white)(".")1color(white)("."))+1/3#

#16/3 ->color(white)("dddd")5 1/3#

#16/3-=color(white)("d")5+0.3bar3#

#16/3-=color(white)("d")5.3bar3#

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