How do you write 3 5/6 as a decimal number rounded to four decimal places?

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Answer 1 · 2016-12-07T17:55:06

#3.8333# to 4 decimal pplaces

#color(red)("Not using a calculator")#

#color(purple)("Doing this a sort of cheating way")#

Method:
Known that #1/3xx1/2=1/6#

so #5xx(1/3xx1/2)=5/6#

#color(green)((5xx1/3))color(red)(xx1/2)=5/6#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write as #3+5/6#

#color(green)("Consider just the "5/3#

#color(green)("It is known that "1/3 = 0.33333....)#

#color(green)("so "5xx1/3 = 5xx0.3333....)#

#color(green)(=1.666666...)#

#color(red)("Now consider the "xx1/2)#

#color(red)(1.66666..xx1/2=0.83333..." "=" "5/6)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

#3 + 5/6 = 3+0.83333... = 3.83333....#

Rounded to 4 decimal places gives

#3.8333#