#color(red)("This is why people say 'divide the 9 into the 8'")#
#color(blue)("What a decimal is:")#
decimals are of form:
#(1/10" of 1 ")+(1/100" of 1 ")+(1/1000" of 1 ")+...#
and so on.
So as an example 0.351 is:
#(3/10" of 1 ")+(5/100" of 1 ")+(1/1000" of 1 ")#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("How we get the answer")#
So we need to change #8/9# to "something of 1"
In other words we change the 9 into 1 and whatever we did to the 9 we also do to the 8
#9xx1/9 = 1#
So #8/9-=(color(red)(8xx1/9))/(9xx1/9) = (0.888888...)/1" "=0.8888888.."going on for ever"#
#color(green)("Notice the "color(red)(8xx1/9))#
#color(green)("This is the same as "8-:9)#
#color(green)("Which is why people say 'just divide the 9 into the 8'")#
#color(purple)("Calculating "8-:9" manually is a different tutorial")#
#color(purple)("and not asked for in the question.")#
