To convert the fraction [tex]\(-\frac{2}{33}\)[/tex] into a decimal, let's follow these steps:
1. Understand the fraction: We have [tex]\(-\frac{2}{33}\)[/tex], which means dividing [tex]\(-2\)[/tex] by [tex]\(33\)[/tex].
2. Perform the division: When you divide [tex]\(-2\)[/tex] by [tex]\(33\)[/tex], the result is a decimal value.
3. Determine the decimal value: Upon careful division, [tex]\(-2 \div 33\)[/tex] gives us [tex]\(-0.06060606060606061\)[/tex].
4. Identify the repeating portion: You will notice that the decimal [tex]\( -0.06060606060606061 \)[/tex] has the repeating portion after the decimal point. Specifically, the digits "06" repeat indefinitely.
5. Express the repeating portion: To correctly write the repeating decimal, we place a bar over the repeating portion. Hence, [tex]\(-\frac{2}{33}\)[/tex] can be expressed as [tex]\( -0.\overline{06} \)[/tex].
So, the answer to the question is:
[tex]\[
-\frac{2}{33} = -0.\overline{06}
\][/tex]
