To determine the nature of the result from the expression \(3.4059... - 853.4059... - 85\), let's analyze the components involved:
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Identifying the Numbers:
- \(3.4059...\) is a repeating decimal, which can be expressed as a fraction (e.g., \(3.4\overline{059}\)).
- \(853.4059...\) is also a repeating decimal, and it can similarly be expressed as a fraction.
- \(85\) is a whole number, which is a rational number.
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Rationality:
- A number is considered rational if it can be expressed as the quotient of two integers (i.e., as a fraction).
- Both \(3.4059...\) and \(853.4059...\) are repeating decimals, thus they are rational numbers.
- The number \(85\) is also a rational number.
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Performing the Calculation:
- When performing operations (addition, subtraction, multiplication, or division) on rational numbers, the result is always a rational number.
Thus, when you calculate \(3.4059... - 853.4059... - 85\), you will get a rational result.
Based on this reasoning, the correct response is:
Rational, because both numbers are rational.
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