Question

a list of numbers is shown below.
-8.5, 2, \\(\frac{2}{3}\\), 0, 6, \\(\frac{3}{4}\\), -246
which venn diagram correctly classifies the list of numbers?
three venn diagrams labeled a, b, c are shown, each classifying numbers into natural (counting) numbers, whole numbers, integers, and rational numbers with different placements for the given numbers

Explanation:

Step1: Recall Number Sets

Natural (counting) numbers: \(1, 2, 3, \dots\) (so \(2, 6\) here). Whole numbers: natural numbers + \(0\) (so \(0, 2, 6\) here). Integers: whole numbers + negatives (so \(-246, 0, 2, 6\) here). Rational numbers: all fractions/decimals that terminate/repeat (all given numbers: \(-8.5, 2, \frac{2}{3}, 0, 6, \frac{9}{4}, -246\) are rational).

Step2: Analyze Each Venn Diagram

• Option A: Check if \(-246\) is in whole numbers? No, whole numbers don't include negatives. So A is wrong.
• Option B: \(-246\) is in integers (correct, integers include negatives), \(0, 2, 6\) in whole numbers (correct, whole numbers include \(0\) and naturals), \(2, 6\) in natural (counting) numbers (correct). Also, \(-8.5, \frac{2}{3}, \frac{9}{4}\) are in rational but not integers/whole/natural (correct, as they are non-integer rationals). This matches.
• Option C: Diagram structure (with the blue line) and number placement (e.g., \(0\) in natural? No, natural numbers start at \(1\)) is incorrect.

Answer:

B. Option Text (the Venn diagram where \(-246\) is in integers, \(0, 2, 6\) in whole numbers, \(2, 6\) in natural (counting) numbers, and non-integer rationals like \(-8.5, \frac{2}{3}, \frac{9}{4}\) are in rational but outside integers/whole/natural)