Question

A manufacturer determines that the cost of making a computer component is ​$2.232323. Write the repeating decimal cost as a fraction and as a mixed number.

Answer 1

Answer:

$\frac{221}{99}$, which as a mixed number is $2\frac{23}{99}$

Step-by-step explanation:

Let's say n = 2.232323... (our repeating decimal. In order to write our decimal number as a fraction, we need to find some way to get rid of the repeating decimal. We can do that by multiplying our number by 100:

100n = 100*2.232323... = 223.232323...

Now, we can set up a system of equations and subtract n from 100n:

$100n=223.232323...\\n=2.232323...\\(100n-n)=223.232323...-2.232323...\\99n=221\\n=\frac{221}{99}$

When we subtracted the two equations, we ended up eliminating the repeating decimal and we were able to solve for n in fraction form. The improper fraction is 221/99

We are also asked to write this as a mixed number. We know that 99*2 is 198. 221 - 198 is 23, which means 221/99 is 2 with a remainder of 23. We can re-write this as a fraction to get the following:

$2\frac{23}{99}$

Answer 2

221/99 or 2 and 23/99