Overview: What Are Rational Numbers?
Rational numbers are numbers that can be expressed as a fraction, a/b, when b is not equal to zero. Both a and b are integers, and rational numbers can be either positive or negative. Rational numbers can take part in mathematical operations of addition, subtraction, multiplication, and division.
What Are Some Types of Rational Numbers?
Types of rational numbers include decimals, percentages, fractions, and ratios. For example, .75, 75%, 3/4, and 3:4, all represent the same relationship. The decimal .75 stands for 75/100, which is the same as 75%. A fraction such as 75/100 can be reduced to simplest terms by dividing by 25/25. The fraction 25/25 itself (which means the same thing as 1) is also a rational number. Rational numbers also include the integers, which can be represented as fractions such as 2/1, 3/1, and so on.
What Are Terminating Decimals?
Many rational numbers can be written as decimals that have a finite number of decimal places. The fraction 1/8 can be written in decimal form as .125, 3/8 in decimal form as .375, and 5/8 as .625. This is in addition to decimals such as .75 for 3/4 or .5 for 1/2. If .75 were carried to 3 decimal places it would be .750, or 750/1000 in fractional form. Similarly, .5 to 2 decimal places would be .50, or 50/100.
What Are Repeating Decimals?
Other rational numbers can be written as repeating decimals with an infinite number of decimal places. For example, the fraction 1/3 can be written as the decimal .33…,which repeats an infinite number of times. If the decimal were .33 and terminated, it would equal 33/100, which is not the same thing. Similarly, the fraction 1/11 is .090909…, in decimal form, which is not the same thing as the terminating .09, equal to 9/100.
What Does the Density of Rational Numbers Mean?
Between any two rational numbers on the number line, there is always another rational number, referred to as the density of rational numbers. The number 2 is a rational number that can represented by 2/1 , and the number 3 is a rational number, represented by 3/1, Between the 2 and the 3 is 2 1/2, between the 2 and the 2 1/2 is 2 1/4, between 2 and 2 1/4 is 2 1/8, and so on. The series never ends.
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