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What is -0.5(3 repeating) written as a fraction?

Answer 1

#-5.333bar3 = -16/3#

Lets for simplicity initially ignore the minus sign.

Let #x=5.33333...# therefore #color(white)("XXX")10x=53.33333...# from which is follows that #color(white)("XXX")9x = 53.3333... - 5.3333... =48# and (dividing by #9#) #color(white)("XXX")x=48/9 = 16/3#

If #5.3333... = x = 16/3# then #-5.3333... = -16/3#

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Answer 2

Avery Alexander

-0.5(3 repeating) can be expressed as a fraction by first representing it as -0.5 + 0.3 repeating. Then, recognizing that 0.3 repeating is equivalent to 1/3, the expression becomes -0.5 + 1/3. Combining these fractions, we get -1/2 + 1/3. To add these fractions, we need a common denominator, which is 6. So, -1/2 becomes -3/6, and 1/3 remains as 1/3. Adding these fractions, we get (-3/6) + (1/3) = -3/6 + 2/6 = -1/6. Therefore, -0.5(3 repeating) written 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.