Question

• use the names of the sets to label the regions. • place the numbers in the correct regions.

names of the sets
integers
rational numbers
whole numbers
numbers
6
19
\\(\frac{4}{5}\\)
\\(-8.\overline{09}\\)
-42

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 \(a,b\in\mathbb{Z}, b
eq0\) (includes integers, fractions, terminating/repeating decimals).

Step2: Identify whole numbers

Whole numbers: \(6, 19\) (since they are non - negative integers).

Step3: Identify integers (excluding whole numbers? No, whole numbers are integers. Integers also include negative integers)

Integers: \(6, 19, - 42\) (whole numbers are integers, and \(-42\) is a negative integer).

Step4: Identify rational numbers

Rational numbers: All given numbers. \(\frac{4}{5}\) is a fraction, \(- 8.\overline{09}\) is a repeating decimal, \(6,19,-42\) are integers (hence rational).

Step5: Label regions

• Innermost circle (Whole numbers): Place \(6, 19\) (since whole numbers are a subset of integers, which are a subset of rational numbers).
• Region between inner (Whole) and middle (Integers) circle: Wait, actually, the inner circle is Whole numbers, the middle (larger) circle is Integers. So the region of Integers not in Whole numbers: \(-42\) (since \(-42\) is an integer but not a whole number).
• Region of Rational numbers not in Integers: \(\frac{4}{5}, - 8.\overline{09}\) (these are rational but not integers). The outermost region (if any, but here the big circle is Rational numbers? Wait, the Venn diagram: inner circle (Whole numbers) is inside middle circle (Integers), which is inside the big circle (Rational numbers).

So:

• Whole numbers (inner circle): \(6, 19\)
• Integers (middle circle, outside whole numbers): \(-42\)
• Rational numbers (big circle, outside integers): \(\frac{4}{5}, - 8.\overline{09}\)

Answer:

• Whole numbers (inner circle): \(6, 19\)
• Integers (between whole and rational): \(-42\)
• Rational numbers (outside integers): \(\frac{4}{5}, - 8.\overline{09}\)

(If we consider the labels: Let the inner circle be Whole numbers, the middle circle (containing inner) be Integers, and the outermost (containing middle) be Rational numbers. Then place the numbers as above in their respective regions.)