To determine whether the sum of \( \frac{3}{4} \) and \( 10^2 \) is irrational, we first need to calculate the values of these two components.
-
Calculate \( 10^2 \): \[ 10^2 = 100 \]
-
Now, add \( \frac{3}{4} \) and \( 100 \): \[ \frac{3}{4} + 100 = \frac{3}{4} + \frac{100 \times 4}{4} = \frac{3}{4} + \frac{400}{4} = \frac{3 + 400}{4} = \frac{403}{4} \]
-
The result \( \frac{403}{4} \) is a rational number since it can be expressed as the ratio of two integers (403 and 4).
Thus, the sum of \( \frac{3}{4} \) and \( 10^2 \) is rational, not irrational.
In one sentence: The sum \( \frac{403}{4} \) is rational because it can be expressed as the quotient of two integers.