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Why are percents rational numbers?

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  • Last Updated : 30 Jun, 2022

Rational numbers are the numbers or fractions that can be written in the form p/q, where m and n are integers and (n≠ 0). Because of the different properties of numbers, the m/n form, most people have difficulty distinguishing between fractions and rational numbers. When a rational number is simplified or divided then the result will be in form of a decimal which can either be terminating or recurring.

Rational numbers include 9, -4, 5, -10, 13, and so on, which can be represented in fraction form as 9/1, -4/1, and 13/1, respectively. A rational number belongs to the real number with the formula m/n, where n is not equal to zero (n ≠ 0). When you divide a rational number, you get a decimal number that can be ended or repeated infinitely. 

Percentage

A percentage is a number or ratio represented as a fraction of one hundred. If we need to compute the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage is known as part per hundred. The term % refers to one hundred percent. It is denoted by the sign “(% percent”).

Examples of Percent are : 10 % , 20 % , 0.5 % etc 

Convert Percentage to fraction

A percent is a ratio or fraction in which the whole is always considered to be 100. So, 4% implies 4 parts out of 100, and 15% indicates 15 parts out of 100. A decimal is a precise way of expressing numbers using a decimal point.

To convert a percentage to a decimal, move the decimal point two positions to the left and remove the percent sign ( %). 

For example, if 2 percent is stated, the decimal equivalent is 0.02.

Let us convert 40% to decimal form. Without the percent symbol, 40% may be written as 40. 

Because it is now a whole number, consider the decimal point on the right end. 40 is equivalent to 40.0. We get 0.4 by moving the decimal point two places to the left. 

As a result, 40% = 0.4.

In the case of a decimal percent, such as 3.5 percent, we must move the decimal point two places to the left. 

As a result, 3.5 percent = 0.035. 

Question: Why are percents rational numbers? 

Answer:

Percents are rational numbers because rational numbers are the numbers that can be expressed in form of fraction , or if divided then the result after decimal it can be either recurring or terminating therefore, a percentage is a number or ratio represented as a fraction of one hundred . and all percent numbers can be expressed in form of fraction, thus they are rational numbers.

hence, 10 % can be written as 10/100 , it is in the form of fraction, therefore its a rational number. 

Sample Problems

Problem 1:  Determine whether 3.5 % is a rational number.

Solution:

A rational numbers are the numbers that can be expressed in form of fraction , or if divided then the result after decimal it can be recurring or terminating .

Here, the given number here 3.5 % can be expressed in form of fraction i.e 35/1000

Hence, 3.5 % is a rational number.

Problem 2: Is  11 % a rational number or an irrational number?

Solution:

A rational numbers are the numbers that can be expressed in form of fraction , or if divided then the result after decimal it can be recurring or terminating .

Here, the given number, 11 % can be expressed in the form of fraction i.e 11/100 

Hence, 11 % is a irrational number.

Problem 3: Determine whether – 23 % is a rational number or an irrational number.

Solution:

A rational numbers are the numbers that can be expressed in form of fraction , or if divided then the result after decimal it can be recurring or terminating .

Here, the given number -23 % can be expressed in fraction i.e  -23/100 is a rational number

hence -23% is a rational number .

Problem 4: Is  7% a rational number or not?

Solution:

A rational numbers are the numbers that can be expressed in form of fraction , or if divided then the result after decimal it can be recurring or terminating .

Here, the given number 7% is a rational number as it can be expressed in form of fraction i.e 7/100 .

Problem 5: Determine whether 0.5 % is a rational number or an irrational number.

Solution:

A rational numbers are the numbers that can be expressed in form of fraction , or if divided then the result after decimal it can be recurring or terminating .

Here, the given number 0.5 % can be expressed in fraction i.e  as 5/1000 is a rational number

hence  0.5 % is a rational number .

Problem 6: Determine whether 2.7 % is a rational number or an irrational number.

Solution:

A rational numbers are the numbers that can be expressed in form of fraction , or if divided then the result after decimal it can be recurring or terminating .

Here, the given number 2.7 % can be expressed in fraction i.e  27/1000 is a rational number

hence 2.7 % is a rational number .

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