How do you convert -0.16 (6 being repeated) to a fraction?

Answer 1

Ethan Adkins

#-13/18#

#color(red)("Note that this is a negative number")#

Write as #(-1) xx 0.16bar6#

Let #x=0.16bar6#

Then #10 x = 1.66bar6#

So #10x-x ->x(10-1) -> 9x= 1.66bar6# #" "ul(0.16bar6) larr" Subtract"#

#9x=1.5#

Double both sides#" "18x=3#

Each of the two sides is divided by 18.

#x=3/18#

But this now needs to be# (-1)xx3/18 = -3/18#

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Answer 2

Eva Adamson

To convert -0.16(6) to a fraction:

Let x = -0.166666...
Multiply x by 100 to move the decimal point two places to the right: 100x = -16.6666...
Subtract x from 100x to eliminate the repeating decimals: 100x - x = -16.6666... - (-0.1666...) = -16.666... + 0.1666... = -16.5
Solve for x: 100x - x = 99x = -16.5
Divide both sides by 99: x = -16.5 / 99
Simplify the fraction: x = -1/6

Therefore, -0.16(6) as a fraction is -1/6.

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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.