High School

How do you write [tex]-93 \frac{1}{6}[/tex] as a decimal?

A. [tex]93.\overline{3}[/tex]

B. [tex]93.1\overline{6}[/tex]

C. [tex]-93.\overline{3}[/tex]

D. [tex]-93.1\overline{6}[/tex]

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].