Final answer:
The numbers 3.14, 1/4, and -3/4 can be identified as follows: 3.14 is rational if considered purely as given, since it can be expressed as a fraction 314/100. Both 1/4 and -3/4 are rational numbers because they can be represented as fractions with integers.
Step-by-step explanation:
To identify whether the numbers 3.14, 1/4, and -3/4 are rational or irrational, we should first understand the definitions of these terms. A rational number is one that can be expressed as a fraction of two integers, where the denominator is not zero. An irrational number cannot be expressed as such a fraction and has a decimal expansion that does not terminate or repeat.
Now, let's analyze each number:
3.14 - This appears to be a truncated version of the number Pi (π). Assuming it is meant to be an approximation of Pi, then in a strict mathematical context, this would be considered irrational. However, 3.14 itself, as a decimal, can actually be expressed as a fraction (314/100), which makes it rational.
1/4 - This is a fraction representing one quarter, and it can be expressed simply as 0.25. Since it can be expressed as a fraction, it is a rational number.
-3/4 - This is a fraction representing negative three quarters, and like 1/4, it is a rational number because it can be represented by -0.75, a terminating decimal.
It's important to build an intuition for fractions and how they represent parts of a whole. Remembering rough estimates like recognizing that roughly π≈3 and using that for practical purposes can make dealing with numbers less daunting and more natural.