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Rational Number

A rational number is any number that can be expressed in the form p/q, where p and q are integers and q is not equal to zero. In decimal form, rational numbers are either terminating or non-terminating but repeating.

Key Concepts

The numerator p and denominator q are typically expressed in their simplest form, meaning they are co-prime integers with no common factor other than 1.

A rational number has a terminating decimal expansion if the prime factorization of its denominator q is of the form 2^n times 5^m, where n and m are non-negative integers.

If the prime factorization of q contains prime factors other than 2 or 5, the rational number will have a non-terminating repeating decimal expansion.

Formula & Equation

p/q, where q is not equal to 0

p represents the numerator which is an integer, and q represents the denominator which is a non-zero integer.

Common Misconceptions

Myth: Integers like 5 or -3 are not rational numbers because they do not look like fractions.

Fact: Every integer is a rational number because it can be written with a denominator of 1, such as 5/1 or -3/1.

Real World Applications

Dividing a pizza into 8 equal slices and taking 3 slices represents the rational number 3/8.

Calculating a batting average in cricket, such as 45 runs in 2 matches, gives the rational number 45/2 or 22.5.

Frequently Asked Questions

Is zero a rational number?

Yes, zero is a rational number because it can be written in the p/q form as 0/1, 0/5, or with any other non-zero denominator.

How do you know if a rational number is terminating or non-terminating?

Check the prime factorization of the denominator in its simplest form. If it only has factors of 2 and 5, it terminates; otherwise, it is non-terminating repeating.

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