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A manufacturer determines the cost of making a computer component is $3.232323 write the repeating decimal cost as a fraction and as a mixed number

User ProdoElmit
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1 Answer

24 votes
24 votes

Answer:

  • $320/99
  • $3 23/99

Explanation:

You want the repeating decimal cost ...


\$3.\overline{23}

written as a fraction and as a mixed number.

Fraction

One can convert the repeating decimal to a fraction by multiplying it by a power of 10 equal to the number of repeating digits.

This cost number (C) has 2 repeating digits (23), so we want to multiply it by 10^2:


100C=10^2*3.23\overline{23}=323.\overline{23}

Now, we can subtract the original cost to cancel the repeating decimal fraction:


100C -C = 323.\overline{23}-3.\overline{23}=320

Dividing by the coefficient of C, we have the fraction we want:


C=\boxed{(320)/(99)}

Mixed number

This is expressed as a mixed number by figuring the quotient and remainder.


(320)/(99)=\boxed{3(23)/(99)}

User Alexbclay
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