Answer :
To convert the mixed number [tex]\(-93 \frac{1}{6}\)[/tex] into a decimal, let's follow these steps:
1. Understand the Components: The number [tex]\(-93 \frac{1}{6}\)[/tex] consists of the whole number [tex]\(-93\)[/tex] and a fractional part [tex]\(\frac{1}{6}\)[/tex].
2. Convert the Fraction to a Decimal: We need to convert [tex]\(\frac{1}{6}\)[/tex] into a decimal. When you divide 1 by 6, it gives approximately [tex]\(0.166666...\)[/tex], which is a repeating decimal. The digit 6 repeats indefinitely.
3. Combine Whole Number and Decimal: Add the decimal [tex]\(0.16666...\)[/tex] to the whole number part [tex]\(-93\)[/tex]. This gives us [tex]\(-93.16666...\)[/tex].
4. Identify the Repeating Part: Since [tex]\(0.16666...\)[/tex] is a repeating decimal, we can express it as [tex]\(0.1\overline{6}\)[/tex]. Therefore, [tex]\(-93 \frac{1}{6}\)[/tex] as a decimal is [tex]\(-93.1\overline{6}\)[/tex].
So, the correct way to write [tex]\(-93 \frac{1}{6}\)[/tex] as a decimal is [tex]\(-93.1\overline{6}\)[/tex]. This corresponds to option [tex]\(-93.1 \overline{6}\)[/tex].
1. Understand the Components: The number [tex]\(-93 \frac{1}{6}\)[/tex] consists of the whole number [tex]\(-93\)[/tex] and a fractional part [tex]\(\frac{1}{6}\)[/tex].
2. Convert the Fraction to a Decimal: We need to convert [tex]\(\frac{1}{6}\)[/tex] into a decimal. When you divide 1 by 6, it gives approximately [tex]\(0.166666...\)[/tex], which is a repeating decimal. The digit 6 repeats indefinitely.
3. Combine Whole Number and Decimal: Add the decimal [tex]\(0.16666...\)[/tex] to the whole number part [tex]\(-93\)[/tex]. This gives us [tex]\(-93.16666...\)[/tex].
4. Identify the Repeating Part: Since [tex]\(0.16666...\)[/tex] is a repeating decimal, we can express it as [tex]\(0.1\overline{6}\)[/tex]. Therefore, [tex]\(-93 \frac{1}{6}\)[/tex] as a decimal is [tex]\(-93.1\overline{6}\)[/tex].
So, the correct way to write [tex]\(-93 \frac{1}{6}\)[/tex] as a decimal is [tex]\(-93.1\overline{6}\)[/tex]. This corresponds to option [tex]\(-93.1 \overline{6}\)[/tex].
