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How do you convert -5.7 (7 repeating) as a fraction?

Answer 1

#a=5 7/9#

Let the required number be #a =- 5.dot7# .....(1) Multiply both sides with #10#, as there is one repeating digit therefore multiply with #10^1# #10a = -57.dot 7# .....(2)

Removing (1) from (2)

#10a - a = -57.dot 7 - (-5. dot7)# #=>9a = -57.dot 7 +5. dot7#

or #9a = -52#

Solving for the required fraction #a = 52/9=5 7/9#

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Answer 2

Avery Alexander

To convert (-5.7\overline{7}) to a fraction, consider it as (x). Then, multiply (x) by (10) to shift the repeating decimal one place to the right, resulting in (10x = -57.\overline{7}). Subtract (x) from (10x) to eliminate the repeating part, giving (10x - x = 9x = -57). Solve for (x) to find (x = -\frac{57}{9} = -\frac{19}{3}). Thus, (-5.7\overline{7}) as a fraction is (-\frac{19}{3}).

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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.