Why is 3/4 + 3.1622 irrational

1 answer

To determine whether the expression \( \frac{3}{4} + 3.1622 \) is irrational, we need to analyze the two components involved:

  1. Rational Numbers: A number is classified as rational if it can be expressed as the ratio of two integers. Since \( \frac{3}{4} \) is a fraction of two integers (3 and 4), it is a rational number.

  2. Decimal Representation: The number \( 3.1622 \) is a terminating decimal. Terminating decimals can also be expressed as a fraction (in this case, \( 3.1622 = \frac{31622}{10000} \)), which means \( 3.1622 \) is also a rational number.

When we add two rational numbers, the result is also a rational number. Specifically:

\[ \frac{3}{4} + 3.1622 = \frac{3}{4} + \frac{31622}{10000} \]

This sum can be calculated to also produce another rational number. Therefore, \( \frac{3}{4} + 3.1622 \) is rational, not irrational.

In conclusion, the statement that \( \frac{3}{4} + 3.1622 \) is irrational is incorrect; it is a rational number.