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What is the original fraction of 0.148148148

User Nurys
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2 Answers

6 votes

Final answer:

The original fraction of the repeating decimal 0.148148148... is found using algebra and the concept of a geometric series, resulting in the fraction 148/999.

Step-by-step explanation:

The original fraction of the repeating decimal 0.148148148... can be found by recognizing it as a geometric series and using algebra to solve for the fraction.

Step 1:

Let x = 0.148148148...

Step 2:

Multiply x by 1000 because the repeating part has three digits: 1000x = 148.148148...

Step 3:

Subtract the original x from this result to get: 1000x - x = 148.148148... - 0.148148148...

Step 4:

This simplifies to: 999x = 148, now divide both sides by 999 to find x.

Step 5:

The fraction is x = 148/999.

Therefore, the original fraction of 0.148148148... is 148/999.

User Hassen
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8.4k points
0 votes
that would be 148148148/1
User Jassuncao
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