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The natural numbers (ℕ) are the counting numbers {1, 2, 3, ...} (though some definitions also include zero: 0) which are whole numbers with no decimal part.

Every rational number (ℚ) can be expressed as one integer (p) over another integer (q): p/q where q cannot be 0.

The rational numbers can be converted to decimal representation by dividing the top number (p) by the decimal number (q): p/q = p ÷ q.

When q = 1, this produces the rational numbers: p/1 = p ÷ 1 = p which is just an integer; it could be one of {[0,] 1, 2, 3, ...} - the natural numbers above: thus all natural numbers are rational numbers.

When q = 2, and p = 1, this produces the rational number 1/2 = 1 ÷ 2 = 0.5 which is not one of the natural number above - so some rational numbers are not natural numbers, thus all rational numbers are not natural numbers.

Thus ℕ ⊂ ℚ (the set of natural numbers is a proper subset of the set of rational numbers).

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Q: Explain why every natural number is also a rational number but not every rational number is a natural number?

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Yes it is, but not every real number is a rational number

Close. But to make that statement correct, three letters must be deleted:Every natural number is a[n ir]rational number.

No. Though every perfect square is a rational number, not every rational number is a perfect square. Example: 2 is a rational number but sqrt(2) is not rational, so 2 is not a perfect square.

Every rational number does.

Every rational number does.

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No. 1/2 is a rational number but it is not a natural number.

Every whole number is rational and an integer. But the "natural" numbers are definedas the counting numbers, so the negative whole numbers wouldn't qualify.No and yes: it is not a natural number but it is a rational number.

No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.

Yes.

Any, and every, irrational number will do.

No because they are rational numbers

No. Every rational number is not a whole number but every whole number is a rational number. Rational numbers include integers, natural or counting numbers, repeating and terminating decimals and fractions, and whole numbers.

Every irrational number is NOT a rational number. For example, sqrt(2) is irrational but not rational. A natural number is a counting number or a whole number, such as 1, 2, 3, etc. A rational number is one that can be expressed as a ratio of two whole numbers, which may be positive or negative. So, -2 is a rational number but not a counting number (it is an integer, though). Also, 2/3 is a rational number but not a whole, counting number or a natural number.

Every integer is a rational number.

well every integer fraction whole number natural number are rational number's surely rational numbers are represented on a number line and as rational numbers are the real numbers

Yes it is, but not every real number is a rational number

No but every integer is a rational number and numbers that can be expressed as fractions are also rational numbers

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