Question

use the names of the sets to label the regions. place the numbers in the correct regions. names of the sets numbers: -0.07, 0, -5.7, \\(\frac{9}{8}\\), 26. venn diagram with sets: rational numbers (outer), integers (middle circle), whole numbers (inner circle).

Explanation:

Step1: Recall number set definitions

• Whole numbers: Non - negative integers (\(0, 1, 2, 3, \dots\))
• Integers: Whole numbers and their negatives (\(\dots, - 2, - 1, 0, 1, 2, \dots\))
• Rational numbers: Numbers that can be expressed as \(\frac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b

eq0\) (includes integers, fractions, terminating and repeating decimals)

Step2: Classify each number

• Whole numbers (and also integers, rational numbers): \(0\), \(26\) (since they are non - negative integers)
• Integers (but not whole numbers): \(- 10\) (negative integer, not a whole number as whole numbers are non - negative)
• Rational numbers (not integers): \(-5.\overline{7}\) (repeating decimal, can be written as a fraction), \(\frac{9}{8}\) (fraction)

Answer:

• Whole numbers (and integers, rational numbers) region: \(0\), \(26\)
• Integers (not whole numbers) region: \(-10\)
• Rational numbers (not integers) region: \(-5.\overline{7}\), \(\frac{9}{8}\)
• Outside all (but since all given numbers are rational, this region is empty for these numbers)