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How do you write 8/9 as a decimal?

Answer 1

Avery Alexander

0.888888....

#color(red)("This is why people say 'divide the 9 into the 8'")#

#color(blue)("What a decimal is:")#

Decimals have the following form:

#(1/10" of 1 ")+(1/100" of 1 ")+(1/1000" of 1 ")+...# and so on.

Thus, 0.351 is an example of:

#(3/10" of 1 ")+(5/100" of 1 ")+(1/1000" of 1 ")# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

"How we get the answer" in blue color.

So we need to change #8/9# to "something of 1"

Stated differently, we convert the 9 into 1, and we apply the same actions to the 8 that we did to the 9.

#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.")#

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Answer 2

Hazel Anglin

0.888...

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.