Question

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. {-9, -4/5, 0, 0.25, √3, 9.2, √100}

Accepted Answer

Step 1: Understand the definitions of each type of number:
- Natural numbers: positive integers starting from 1 (1, 2, 3, ...).
- Whole numbers: natural numbers including zero (0, 1, 2, 3, ...).
- Integers: all whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...).
- Rational numbers: numbers that can be expressed as a fraction $$ \frac{a}{b} $$ where $$a$$ and $$b$$ are integers and $$b 
eq 0.
- $$Irrational numbers: numbers that cannot be expressed as a simple fraction, their decimal expansions are non-terminating and non-repeating.
- Real numbers: all rational and irrational numbers combined. Step 2: Evaluate each element in the set $$ \{-9, -\frac{4}{5}, 0, 0.25, \sqrt{3}, 9.2, \sqrt{100} \} $$:
- $$-9 is an $$integer.
- $$-\frac{4}{5} is a $$rational number (fraction).
- $$0 is a $$whole number.
- $$0.25 is a $$rational number (can be written as $$\frac{1}{4}$$).
- $$\sqrt{3} is an $$irrational number.
- $$9.2 is a $$rational number (can be written as $$\frac{92}{10}$$).
- $$\sqrt{100}$$ simplifies to $$10$$, which is a natural number. Step 3: List all natural numbers from the set:
- Identify numbers that are positive integers starting from 1.
- From the set, $$10 ($$from $$\sqrt{100}) is a $$natural number. Step 4: List all whole numbers from the set:
- Include all natural numbers and zero.
- From the set, $$0$$ and $$10 ($$from $$\sqrt{100}) $$are whole numbers. Step 5: List all integers, rational numbers, irrational numbers, and real numbers:
- Integers: numbers without fractional parts, including negatives and zero ($$-9, 0, 10).
- $$Rational numbers: all numbers that can be expressed as fractions ($$-9, -\frac{4}{5}, 0, 0.25, 9.2, 10).
- $$Irrational numbers: numbers that cannot be expressed as fractions ($$\sqrt{3}).
- $$Real numbers: all numbers in the set since they are either rational or irrational.

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. {-9, -4/5, 0, 0.25, √3, 9.2, √100}

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