Question

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

Answer 1

• $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)}`