answersLogoWhite

0


Best Answer

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).

User Avatar

Wiki User

βˆ™ 2014-08-06 10:47:25
This answer is:
User Avatar
Study guides

Algebra

20 cards

A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

➑️
See all cards
3.8
β˜†β˜…β˜†β˜…β˜†β˜…β˜†β˜…β˜†β˜…
1474 Reviews

Add your answer:

Earn +20 pts
Q: Explain why every natural number is also a rational number but not every rational number is a natural number?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

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.


Every natural numaber is a rational number?

Yes.


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.


Can every natural number be an irrational number?

No because they are rational numbers


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.


Is every integer a rational number or is every rational number an integer?

Every integer is a rational number.


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


Every rational number is a real number?

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


Is every number a rational number?

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

People also asked