How do you use long division to determine the decimal equivalent of 5/9?

1 Answer
Sep 16, 2017

#50 div5# gives an answer of #5# with a remainder of #5# each time.

#5/9 = 0.55555...... = 0.dot5#

Explanation:

The fraction #5/9# means #5 div 9##color(white)(www)9 |bar(5.0000000......)#

#color(white)(wwwww)0.5color(white)(aaaaaaaa)larr 5div 9=0, 50div9=5#
#color(white)(www)9 |bar(5.0000000......)#
#color(white)(wwwww)ul4.5" "larr 0.5 xx 9#
#color(white)(wwwww)0.50" "larr# subtract, bring down a #0#

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Same process again:

#color(white)(wwwww)0.55color(white)(aaaaaaaa)larr 50div9=5#
#color(white)(www)9 |bar(5.0000000......)#
#color(white)(wwwww)ul4.5#
#color(white)(wwwww)0.50#
#color(white)(ww.www)ul.45#
#color(white)(ww.www).050" "larr# subtract, bring down a #0#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Same process again and again:

#color(white)(wwwww)0.555555color(white)(aaaaaaaa)larr 50div9=5#
#color(white)(www)9 |bar(5.0000000......)#
#color(white)(wwwww)ul4.5#
#color(white)(wwwww)0.50#
#color(white)(ww.www)ul.45#
#color(white)(ww.www).050#
#color(white)(ww.www)ul.045#
#color(white)(ww.www).0050" "larr# subtract, bring down a #0#