Final answer:
To convert the decimal 1.083333333333333 to a fraction, identify the repeating decimal part, set up an equation to eliminate the repeat, simplify, and express the result as a fraction. The answer is 13/12.
Step-by-step explanation:
Converting the decimal 1.083333333333333 to a fraction involves recognizing that the decimal portion is a repeating decimal. The number 0.083333333333333... repeats indefinitely, and the repeating digit is 3. To convert this repeating decimal to a fraction, we follow these steps:
- Represent the repeating decimal as x: x = 0.08333...
- Multiply x by 10 to shift the decimal point one place to the right, leading to 10x = 0.83333....
- Subtract the original x from this new equation to get 9x = 0.7500.
- Now, solve for x by dividing both sides of the equation by 9: x = 0.08333... = 0.75/9.
- Since 0.75 is the same as 75/100 and we can reduce that to 3/4, we have x = 3/4/9 = 3/36, which simplifies to 1/12.
Finally, to get the fraction for the original decimal including the whole number part, we have 1 + 1/12 which is 13/12 as a fraction.