How do you write 8/9 as a decimal?

1 Answer
Dec 12, 2016

0.888888....

Explanation:

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.")