Final answer:
Due to missing information, an exact answer for the proof cannot be provided. However, typical concepts that could be related include modular arithmetic, scientific notation, and calculating percentages, all of which are common in high school mathematics.
Step-by-step explanation:
It seems like there are some typos or information missing from the question related to the mathematical proof that needs to be completed. However, based on the context provided, we can deduce that this question is related to modular arithmetic, specifically the proof involving the modulo operation. Perhaps the question aims to prove a property such as 21 <= (mod 242) or something similar.
Unfortunately, without the exact details of the proof required, we cannot provide a complete answer. However, to address the hints and examples given, we can talk about the use of scientific notation and calculating percentages which are common concepts in high school mathematics. For example, expressing a number in scientific notation simplifies the process of dealing with very large or very small numbers, by factoring them into a product of a number and a power of 10.
When it comes to calculating percentages, one method is to set up equivalent fractions where one has a denominator of 100, which makes it easier to understand and manipulate percent values.