Solved on Dec 04, 2023

Determine which set(s) the number $\frac{2}{7}$ belongs to: Natural (N), Whole (W), Integers (I), Rational (Q), Irrational (S), Real (R).

STEP 1

Assumptions
1. The number we are considering is $\frac{2}{7}$ .
2. We are considering the following sets: Natural numbers (N), Whole numbers (W), Integers (I), Rational numbers (Q), Irrational numbers (S), and Real numbers (R).

STEP 2

Let's start by defining each set of numbers:
- Natural numbers (N) are the set of positive integers, starting from 1. They do not include fractions or decimals. - Whole numbers (W) are the set of non-negative integers, starting from 0. They also do not include fractions or decimals. - Integers (I) are the set of whole numbers and their negatives. They do not include fractions or decimals. - Rational numbers (Q) are the set of numbers that can be expressed as a fraction of two integers, where the denominator is not zero. - Irrational numbers (S) are the set of numbers that cannot be expressed as a fraction of two integers. Their decimal representation is non-repeating and non-terminating. - Real numbers (R) are the set of all rational and irrational numbers.

STEP 3

Now, we will check if $\frac{2}{7}$ belongs to the set of Natural numbers (N). Since natural numbers do not include fractions, $\frac{2}{7}$ does not belong to this set.

STEP 4

Next, we will check if $\frac{2}{7}$ belongs to the set of Whole numbers (W). Since whole numbers do not include fractions, $\frac{2}{7}$ does not belong to this set.

STEP 5

Next, we will check if $\frac{2}{7}$ belongs to the set of Integers (I). Since integers do not include fractions, $\frac{2}{7}$ does not belong to this set.

STEP 6

Next, we will check if $\frac{2}{7}$ belongs to the set of Rational numbers (Q). Since rational numbers are the set of numbers that can be expressed as a fraction of two integers, $\frac{2}{7}$ does belong to this set.

STEP 7

Next, we will check if $\frac{2}{7}$ belongs to the set of Irrational numbers (S). Since irrational numbers are the set of numbers that cannot be expressed as a fraction of two integers, $\frac{2}{7}$ does not belong to this set.

STEP 8

Finally, we will check if $\frac{2}{7}$ belongs to the set of Real numbers (R). Since real numbers are the set of all rational and irrational numbers, and $\frac{2}{7}$ is a rational number, $\frac{2}{7}$ does belong to this set.
So, the number $\frac{2}{7}$ belongs to the sets of Rational numbers (Q) and Real numbers (R).

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Determine which set(s) the number $\frac{2}{7}$ belongs to: Natural (N), Whole (W), Integers (I), Rational (Q), Irrational (S), Real (R).

STEP 1

Assumptions
1. The number we are considering is $\frac{2}{7}$ .
2. We are considering the following sets: Natural numbers (N), Whole numbers (W), Integers (I), Rational numbers (Q), Irrational numbers (S), and Real numbers (R).

STEP 2

STEP 3

Now, we will check if $\frac{2}{7}$ belongs to the set of Natural numbers (N). Since natural numbers do not include fractions, $\frac{2}{7}$ does not belong to this set.

STEP 4

Next, we will check if $\frac{2}{7}$ belongs to the set of Whole numbers (W). Since whole numbers do not include fractions, $\frac{2}{7}$ does not belong to this set.

STEP 5

Next, we will check if $\frac{2}{7}$ belongs to the set of Integers (I). Since integers do not include fractions, $\frac{2}{7}$ does not belong to this set.

STEP 6

Next, we will check if $\frac{2}{7}$ belongs to the set of Rational numbers (Q). Since rational numbers are the set of numbers that can be expressed as a fraction of two integers, $\frac{2}{7}$ does belong to this set.

STEP 7

Next, we will check if $\frac{2}{7}$ belongs to the set of Irrational numbers (S). Since irrational numbers are the set of numbers that cannot be expressed as a fraction of two integers, $\frac{2}{7}$ does not belong to this set.

STEP 8

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Determine which set(s) the number 27\frac{2}{7}72​ belongs to: Natural (N), Whole (W), Integers (I), Rational (Q), Irrational (S), Real (R).

STEP 1

Assumptions1. The number we are considering is 27\frac{2}{7}72​.2. We are considering the following sets: Natural numbers (N), Whole numbers (W), Integers (I), Rational numbers (Q), Irrational numbers (S), and Real numbers (R).

STEP 2

STEP 3

Now, we will check if 27\frac{2}{7}72​ belongs to the set of Natural numbers (N). Since natural numbers do not include fractions, 27\frac{2}{7}72​ does not belong to this set.

STEP 4

Next, we will check if 27\frac{2}{7}72​ belongs to the set of Whole numbers (W). Since whole numbers do not include fractions, 27\frac{2}{7}72​ does not belong to this set.

STEP 5

Next, we will check if 27\frac{2}{7}72​ belongs to the set of Integers (I). Since integers do not include fractions, 27\frac{2}{7}72​ does not belong to this set.

STEP 6

Next, we will check if 27\frac{2}{7}72​ belongs to the set of Rational numbers (Q). Since rational numbers are the set of numbers that can be expressed as a fraction of two integers, 27\frac{2}{7}72​ does belong to this set.

STEP 7

Next, we will check if 27\frac{2}{7}72​ belongs to the set of Irrational numbers (S). Since irrational numbers are the set of numbers that cannot be expressed as a fraction of two integers, 27\frac{2}{7}72​ does not belong to this set.

STEP 8

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine which set(s) the number $\frac{2}{7}$ belongs to: Natural (N), Whole (W), Integers (I), Rational (Q), Irrational (S), Real (R).

Assumptions
1. The number we are considering is $\frac{2}{7}$ .
2. We are considering the following sets: Natural numbers (N), Whole numbers (W), Integers (I), Rational numbers (Q), Irrational numbers (S), and Real numbers (R).

Now, we will check if $\frac{2}{7}$ belongs to the set of Natural numbers (N). Since natural numbers do not include fractions, $\frac{2}{7}$ does not belong to this set.

Next, we will check if $\frac{2}{7}$ belongs to the set of Whole numbers (W). Since whole numbers do not include fractions, $\frac{2}{7}$ does not belong to this set.

Next, we will check if $\frac{2}{7}$ belongs to the set of Integers (I). Since integers do not include fractions, $\frac{2}{7}$ does not belong to this set.

Next, we will check if $\frac{2}{7}$ belongs to the set of Rational numbers (Q). Since rational numbers are the set of numbers that can be expressed as a fraction of two integers, $\frac{2}{7}$ does belong to this set.

Next, we will check if $\frac{2}{7}$ belongs to the set of Irrational numbers (S). Since irrational numbers are the set of numbers that cannot be expressed as a fraction of two integers, $\frac{2}{7}$ does not belong to this set.