Repeating Decimal As A Series: Worked Example and Solution
A complete geometric-series structure example with method choice, derivation, verification, and a common wrong approach.
1 problem8 min estimated timeFoundational to intermediate progression
Problem
- Write 0.272727… as a fraction.
Complete worked solutions
Every problem has a source-matched answer and independently reviewed derivation.
01
Problem 1: Write 0.272727… as a fraction.
Answer:
Why this method: Geometric-series structure matches the mathematical structure before any algebraic cleanup.
- Write the decimal as .
- This has , , so its sum is .
- Therefore the result is .
What is included
See a concise answer and full derivation for write 0.272727… as a fraction.
Skills assessed
- Geometric-series structure
Prerequisites
- sequences
- sigma notation
Long description
Read the diagram from top to bottom. Each numbered box names one decision or mathematical operation. Arrows show the required order; the text labels remain the complete interpretation in print, dark mode, and nonvisual reading.
Printable and accessible
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Common errors
- Using the infinite-sum formula without checking the common-ratio condition or the starting index.