How do you express 1.33333333333 as a fraction?

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.

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