To express the decimal 1.33333333333 as a fraction, we follow these steps:
First, recognize that the decimal 1.33333333333 can be rewritten as 1.3̅, where the line over the 3 indicates that it repeats indefinitely. We can break this down into two parts: the whole number and the repeating decimal.
1. Start with the value:
- Let x = 1.3̅
2. To eliminate the repeating part, multiply x by 10 because there is only one digit in the repeating part:
- 10x = 13.3̅
3. Now we have two equations:
- x = 1.3̅
- 10x = 13.3̅
4. Next, subtract the first equation from the second equation to eliminate the repeating decimal:
- 10x – x = 13.3̅ – 1.3̅
- 9x = 12
5. Solve for x by dividing both sides by 9:
- x = 12/9
6. This fraction can be simplified. Divide both the numerator and the denominator by 3:
- x = 4/3
7. Finally, since we initially translated 1.3̅ into a fraction, we must now account for the whole number part:
- 1.33333333333 = 1 + 4/3
- = 3/3 + 4/3 = 7/3
Therefore, the decimal 1.33333333333 can be expressed as the fraction 7/3.