2/9 simiplfied into a decimal?

1 Answer
Feb 16, 2018

#2/9 = 2 div 9 = 0.22222222.... = 0.bar2#

Explanation:

#2/9 = 2 div 9#

Do the division:

# 9|ul(2.0000000)" "larr 2 div 9 = 0#
#" "0.#

# 9|ul(2.0^(2)000000)" "larr 20 div 9 = 2# with #2# remaining
#" "0.2#

# 9|ul(2.0^(2)0^(2)00000)" "larr 20 div 9 = 2# with #2# remaining
#" "0.2color(white)(.) 2#

# 9|ul(2.0^(2)0^(2)00000)" "larr 20 div 9 = 2# with #2# remaining
#" "0.2color(white)(.) 2color(white)(.) 2#

This process repeats and the decimal recurs

# 9|ul(2.0^(2)0^(2)0^(2)0^(2)0^(2)0^(2)0......)" "larr 20 div 9 = 2# with #2# remaining
#" "0.2color(white)(.) 2color(white)(.) 2color(white)(.) 2color(white)(.) 2color(white)(.) 2color(white)(.) 2.....#