To express the fraction [tex]\(\frac{5}{6}\)[/tex] as a decimal, follow these detailed steps:
1. Division Setup: Understand that you need to divide the numerator (5) by the denominator (6). Essentially, you're performing the division [tex]\(5 \div 6\)[/tex].
2. Perform the Division:
- [tex]\(6\)[/tex] goes into [tex]\(5\)[/tex] zero times, so start with [tex]\(0.\)[/tex].
- Next, add a decimal point and bring down a zero to make it [tex]\(50\)[/tex].
- Determine how many times [tex]\(6\)[/tex] goes into [tex]\(50\)[/tex]. [tex]\(6\)[/tex] fits into [tex]\(50\)[/tex] eight times because [tex]\(6 \times 8 = 48\)[/tex].
- Subtract [tex]\(48\)[/tex] from [tex]\(50\)[/tex] to get a remainder of [tex]\(2\)[/tex], and bring down another zero to make it [tex]\(20\)[/tex].
- Determine how many times [tex]\(6\)[/tex] goes into [tex]\(20\)[/tex]. [tex]\(6\)[/tex] fits into [tex]\(20\)[/tex] three times because [tex]\(6 \times 3 = 18\)[/tex].
- Subtract [tex]\(18\)[/tex] from [tex]\(20\)[/tex] to get a remainder of [tex]\(2\)[/tex], and bring down another zero to make it [tex]\(20\)[/tex].
3. Repeat the Process: Notice that repeating the process will again fit [tex]\(6\)[/tex] into [tex]\(20\)[/tex] three times, each time giving a remainder of [tex]\(2\)[/tex] and repeating the decimal digits.
4. Conclude the Decimal Representation: This repetitive process reveals that the decimal representation is ongoing. So, the result of dividing [tex]\(5\)[/tex] by [tex]\(6\)[/tex] results in a repeating decimal.
Thus, the decimal representation of [tex]\(\frac{5}{6}\)[/tex] is [tex]\(0.8333333333333334\)[/tex], where the digit [tex]\(3\)[/tex] repeats consistently.
