Positive Rational Numbers

Any number greater than zero and can be represented as a fraction of two integers is a positive rational number. Also remember that the two integers are always positive and the denominator is not equal to zero. For example, ½, 3, 0.75, etc., are positive rational numbers.

No, 0 is not a positive rational number because it is located right in the middle of the number line and is neutral. Positive rational numbers are defined as numbers greater than zero.

Is Every Natural Number a Positive Rational Number?

Yes, every natural number is a positive rational number. Natural numbers like 1, 2, 3, and so on can be written in the form of a rational number by expressing them as fractions with 1 in the denominator (e.g., 2 can be written as 2/1).

Positive Rational Numbers Less Than 1

Positive rational numbers less than 1 are fractions where the numerator is smaller than the denominator. Examples include 1/2, 3/4, 7/10, etc. These numbers are greater than 0 but less than 1. They are used in measuring; for e.g., cooking often requires measuring of ingredients in fractions. 

Positive Rational Numbers: Symbol

There is no unique symbol for positive rational numbers. However, since they are a subset of rational numbers (represented by Q), we can write Q⁺ to represent all rational numbers greater than zero.

Reciprocal of a Positive Rational Number

The reciprocal of a positive rational number is another positive rational number, obtained by flipping the numerator and denominator. Let us consider 1/2 as an example. The reciprocal of 1/2 is 2/1. Whenever a number is multiplied by its reciprocal, the result will always be 1. Every positive rational number has a reciprocal.
 

There are many differences between positive rational numbers and negative rational numbers, the differences are shown below in the table:
 

There are various properties of positive rational numbers, some of them are mentioned below:

• On a number line, the numbers right of 0 are all positive rational numbers. Naturally, they are greater than 0.

• These numbers can be expressed as a fraction where the numerator and the denominator will always be positive.

• When any two positive rational numbers are added or multiplied, the result will always be a positive rational number.

• Positive rational numbers can be represented as recurring or terminating decimals.
   

Positive rational numbers have numerous applications across various fields. Let us check them out one by one:

• Money and Financial Transactions: We use positive rational numbers when we do monetary transactions. Amounts like $5.75 and $28.46 are positive rational numbers. These numbers help in budgeting, calculating interest rates, discounts, taxes, and dividing costs among people. 

• Cooking: If we follow a recipe while cooking, we will often come across measurements like “½ tablespoon of sugar and ¾ cup of water.” These measurements represent positive rational numbers.

• Construction and Architecture: Builders and architects use numbers like 4.5 and 1.25 to measure lengths, widths, and heights. Positive rational numbers play an important role in building edifices.