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.")