To convert the fraction [tex]\(\frac{2}{3}\)[/tex] into a decimal, follow these steps:
1. Understand the Fraction: The fraction [tex]\(\frac{2}{3}\)[/tex] means that you are dividing 2 by 3.
2. Perform the Division:
- Divide 2 by 3. Since 2 is smaller than 3, the division will not go evenly, and we will have to use decimal places.
- Add a decimal point to 2, making it 2.0, and then perform the division.
3. Calculate the Quotient:
- 3 goes into 20 six times because [tex]\(3 \times 6 = 18\)[/tex].
- Subtract 18 from 20, which leaves a remainder of 2.
- Bring down a 0, making it 20 again, and repeat the process.
- This cycle repeats, resulting in the repeating decimal 0.666...
4. Representation in Decimal Form:
- The repeating part of the decimal is 6, so we denote this as [tex]\(0.\overline{6}\)[/tex].
Therefore, the decimal representation of [tex]\(\frac{2}{3}\)[/tex] is [tex]\(0.\overline{6}\)[/tex], where the 6 is the repeating digit.
