When the repeating decimal 0.151515... is written as a fraction in lowest terms, what is that fraction?

Introduction / Context:
This question focuses on converting a repeating decimal with a two-digit repeating block into a fraction. Understanding this method strengthens algebraic manipulation skills and number sense.

Given Data / Assumptions:

• Repeating decimal: 0.151515..., with 15 repeating indefinitely.
• We must express this decimal as a fraction in simplest form.
• The repeating pattern is constant throughout the decimal part.

Concept / Approach:
The standard technique is to assign the decimal to a variable, multiply by a power of 10 equal to the length of the repeating block, and then subtract to eliminate the repeating part. The remaining equation is easy to convert into a fraction.

Step-by-Step Solution:

Verification / Alternative check:
To check, convert 5/33 back to decimal form. 1/33 is approximately 0.030303..., so 5/33 is 5 times that, about 0.151515..., which matches the given decimal.

Why Other Options Are Wrong:
17/33 is approximately 0.515151..., which is too large. 9/11 equals about 0.818181..., with an 81 repeating pattern. 7/33 is about 0.212121..., not 0.151515.... None of these match the required repeating decimal.

Common Pitfalls:
Errors often occur in choosing the correct power of 10 to multiply by, or in simplifying the resulting fraction. Some candidates may incorrectly use 10x instead of 100x, which fails to align the repeating blocks properly.

Final Answer:
The repeating decimal 0.151515... is equal to the fraction 5/33.