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Explain why every natural number is also a rational number but not every rational number is a natural number?
Wiki User
∙ 9y ago
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).
Wiki User
∙ 9y ago
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Every natural number is an irrational number?
Close. But to make that statement correct, three letters must be deleted:Every natural number is a[n ir]rational number.
Every rational number is a real number?
Yes it is, but not every real number is a rational number
Is every rational number a perfect square?
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.
What number produces a rational number when multiplied by .5?
Every rational number does.
Which number produces a rational number when added to 0.25?
Every rational number does.
Is every rational number a natural number?
No. 1/2 is a rational number but it is not a natural number.
Is every whole number a natural integer and a rational 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.
Is every real number is rational?
No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.
Which number can be added to a rational number to explain that the sum of rational number and an irrational number is irrational?
Any, and every, irrational number will do.
Is every rational number a whole number?
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.
Why every irrational number is also a rational number but not every rational number is a natural number?
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.
Can every natural number be an irrational number?
No because they are rational numbers
Can rational numbers be placed on the number line?
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
Are natural numbers whole numbers and integers also rational numbers?
Yes. Every whole number and every whole negative number and zero are all integers.
Is every integer a rational number or is every rational number an integer?
Every integer is a rational number.
Every natural number is an irrational number?
Close. But to make that statement correct, three letters must be deleted:Every natural number is a[n ir]rational number.
What real number is both integer and a natural number?
Real numbers consist of all numbers except complex numbers. Every integer is a natural number but every rational number is not a natural number as well as an integer. So, the answer to the question is integer.
