# Why are percents rational numbers?

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:**

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:**

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:**

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 .