Question

A manufacturer determines that the cost of making a computer componet is $2.131313. Write the repeating decimal cost as a fraction and as a mixed number

Answer 1

To write the repeating decimal cost as a fraction, we can let x = 2.131313...

Then, we multiply both sides of the equation by 100 to eliminate the decimal:

100x = 213.131313...

Next, we subtract the original equation from the equation multiplied by 100:

100x - x = 213.131313... - 2.131313...

Simplifying the right side of the equation gives:

99x = 211

Now, we can solve for x by dividing both sides of the equation by 99:

x = 211/99

Therefore, the repeating decimal cost of making the computer component is 211/99.

To write this as a mixed number, we can divide 211 by 99:

211 ÷ 99 = 2 remainder 13

Thus, the repeating decimal cost can be written as a mixed number: 2 and 13/99.