Converting the Decimal 4.888888888888 to a Fraction

To convert the decimal 4.888888888888 to a fraction, we can follow these steps:

1. Separate the whole number and decimal parts: The decimal 4.888888888888 can be separated into the whole number 4 and the decimal 0.888888888888.
2. Convert the decimal part to a fraction: To convert 0.888888888888 to a fraction, recognize that it is a repeating decimal. We can represent it as: Let x = 0.888888888888...
3. Multiply to eliminate the repeating part: Multiply both sides of the equation by 10, leading to: 10x = 8.888888888888...
4. Subtract the original equation from this new one: This gives: 10x - x = 8.888888888888... - 0.888888888888...
5. Which simplifies to: 9x = 8
6. Now, solve for x: The solution is x = 8/9.
7. Combine the whole number and the fraction: We can now write the full expression as: 4 + 0.888888888888 = 4 + 8/9
8. Convert the whole number 4 to a fraction with a common denominator: We need to express 4 as a fraction: 4 = 36/9.
9. Add the fractions together: Now combine 36/9 + 8/9 = (36 + 8)/9 = 44/9.

Thus, the decimal 4.888888888888 can be expressed as the fraction 44/9.