Question

build a venn diagram. • use the names of the sets to label the regions. • place the numbers in the correct regions. names of the sets whole numbers rational numbers irrational numbers integers numbers 95 -7√11 0.(overline{2}) 4π -√36

Explanation:

Step1: Recall number set definitions

• Integers:..., -3, -2, -1, 0, 1, 2, 3,...
• Whole numbers: 0, 1, 2, 3,... (subset of integers)
• Rational numbers: Numbers that can be expressed as $\frac{p}{q}$ ($q

eq0$, $p,q$ integers) (includes integers, fractions, terminating/repeating decimals).

• Irrational numbers: Numbers that cannot be expressed as $\frac{p}{q}$ (non - repeating, non - terminating decimals, like $\sqrt{2}$, $\pi$).

Step2: Analyze each number

• $-\sqrt{36}$: Simplify $-\sqrt{36}=- 6$, which is an integer (and whole number, rational).
• 95: Whole number (so integer, rational).
• $0.\overline{2}$: Repeating decimal, so rational (can be written as $\frac{2}{9}$), not integer (since it's a fraction between 0 and 1).
• $-7\sqrt{11}$: $\sqrt{11}$ is irrational, multiplying by - 7 keeps it irrational.
• $4\pi$: $\pi$ is irrational, multiplying by 4 keeps it irrational.

Step3: Assign to Venn regions

• Innermost circle (Integers): Contains numbers that are integers. So $-\sqrt{36}=-6$ and 95 (since 95 is a whole number, hence integer).
• Middle circle (Whole numbers): Wait, actually, the middle circle (inside the larger rational circle) should be Whole numbers (subset of Integers? Wait, no: Integers include negative numbers, whole numbers are non - negative integers. Wait, maybe the Venn has:
• Largest circle: Rational numbers (includes Integers, Whole numbers, and non - integer rationals like $0.\overline{2}$).
• Inside Rational: a circle for Integers, and inside Integers: a circle for Whole numbers.
• Separate region: Irrational numbers (outside Rational).

So:

• Irrational region: $-7\sqrt{11}$, $4\pi$ (since they are irrational).
• Rational (but not Integer) region: $0.\overline{2}$ (repeating decimal, rational, not integer).
• Integer (but not Whole number) region: $-\sqrt{36}=-6$ (integer, negative, so not whole number).
• Whole number region (inside Integer): 95 (whole number, so integer, rational).

Answer:

• Irrational numbers (right region): $-7\sqrt{11}$, $4\pi$
• Rational numbers (left large rectangle):
• Rational (not Integer): $0.\overline{2}$
• Integer (not Whole): $-\sqrt{36}$
• Whole numbers (innermost circle): $95$

(To draw the Venn: Label the left large circle as "Rational numbers", inside it a circle "Integers", inside "Integers" a circle "Whole numbers". The right region is "Irrational numbers". Place numbers as above.)