Final answer:
The number 0.121212... is a rational number because it can be represented as the fraction 12/99. Awareness of significant figures is crucial to prevent overestimating precision during mathematical calculations.
Step-by-step explanation:
The real number 0.1212121212... is actually considered a rational number because it can be expressed as the fraction 12/99. The misconception might arise from the belief that repeating decimals are not rational, but this is not true. A repeating decimal is a rational number if it can be written as a fraction of two integers. The way to convert a repeating decimal like 0.121212... to a fraction is by setting it equal to a variable, multiplying by a power of 10 to shift the decimal point, and then subtracting the original equation from this new equation to eliminate the repeating part and solve for the variable.
It is important to be aware of significant figures when dealing with numbers in mathematical operations, especially to avoid overestimating the precision of our results. When adding, subtracting, multiplying, or dividing, rules for significant figures help determine the appropriate number of digits to carry in the answer. This awareness helps prevent the false precision that calculators might suggest, as they display many more digits than the numbers originally had significant figures for.