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Which type of numbers can be written as a fraction plq where p and q are integers and q is not equal to zero?
rational numbers
Explain why every natural number is also a rational number but not every rational number is a natural number?
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).
Difference between rational and irrational?
Rational numbers can be expressed in the form p/q (where q is not equal to zero). Irrational numbers cannot be expressed in this form. For example, the square root of 2 cannot be expressed as p/q.
Is it possible to divide one rational number by another to obtain an irrational number as a quotient?
No. Rational numbers are defined as fractions of whole numbers. Suppose we have two rational numbers A = m/n and B = p/q. Then their quotient is defined as A/B = (m*q) / (n*p). Since m,n,p and q are whole, the products m*q and n*p are whole as well, making A/B a rational number.
What letter is used to notate the set of a rational number?
ℚ (fancy capital Q) is the set of rational numbers.
What is the symbol of a rational number?
The set of rational numbers is represented by Q.
What is the symbol used for irrational numbers?
There is no specific symbol. The symbol for real numbers is R and that for rational numbers is Q so you could use R \ Q.
What is the symbol for rational numbers?
Q is the set of all rational numbers. The letter Q is used because rationals can be expressed as a quotient of two integers. Any letter from the Greek or Latin alphabet may be used as a symbol for an individual rational number.
What is the symbol of irrational numbers?
There is no special symbol.The set of rational numbers is denoted by Q and the set of real numbers by R so one option is R - Q.
What are rational and rational numbers?
Rational numbers are numbers which can be written in the form p/q where p and q are integers and q > 0. Rationals is often used as an abbreviation to refer to the set of all rational numbers.
How will you describe rational numbers?
Rational numbers are numbers which can be expressed as a ratio of two integers, p and q (where q >0), in the form p/q.
Why are rational numbers denoted as Q?
The letter R was used for real numbers. So Q, for quotients was used for rational numbers.
Does Q represent rational numbers?
The letter Q in blackboard bold is used to represent the set of rational numbers - Q standing for quotient.
What are rational numbers but not integers?
The vast majority of rational numbers are not integers. They are numbers which can be written in the form p/q where p and q are integers which are co-prime and q > 1.
What type of numbers are said to be in rational form and are referred to as rational numbers?
They are numbers which are written in the form p/q where p and q are integers.
What is the abbreviation for rational numbers?
Q
Why are whole numbers rational numbers?
rational no. is of the for p/q where p,q are integers & q not equls to 0.Every whole number can be expressed as a rational number as x/1 where x is whole no.
