Determine if 0, point, 3, 4, 3, 7, 50.34375 is rational or irrational and give a reason for your answer.

Answer 1

To determine whether the number \( 50.34375 \) is rational or irrational, we first need to recall the definitions:

• A rational number is any number that can be expressed as the fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).
• An irrational number, on the other hand, cannot be expressed as such a fraction and does not have a repeating or terminating decimal.

Now, let's examine the number \( 50.34375 \):

1. We notice that \( 50.34375 \) is in decimal form.
2. The decimal representation \( 0.34375 \) is terminating, as it ends after a finite number of digits (specifically, it has five digits after the decimal point).
3. Any number with a terminating decimal representation can be expressed as a fraction of two integers.

For example, we can express \( 50.34375 \) as follows: \[ 50.34375 = \frac{5034375}{100000} \] Here \( 5034375 \) and \( 100000 \) are both integers, and \( 100000 \neq 0 \), confirming it meets the criteria for being a rational number.

Thus, we conclude that:

50.34375 is a rational number because it can be expressed as the fraction \( \frac{5034375}{100000} \).