March 29, 2023

# Know How Fractions are Different from Rational Numbers and What Differentiates Percentage From Percentile in Detail

Before diving deep into the Difference Between Fraction and Rational Numbers and the Difference between Percentage and Percentile, let’s understand the concepts of each of these terms separately in detail.

Percentage

The percentage is a numerical value calculated out of a total of 100. The percentage is represented by the symbol ” per cent “. This symbol represents the denominator value of 100. The percentage can be expressed as a fraction or as a decimal. A % is the standard way to differentiate the quantities during the comparison process. It contains information on the ratio and proportions.

Example of Percentage: If a student receives 55 marks in their maths exams out of a total of 100, he or she has received a 55 % aggregate in their math tests. The student received a score of 55 % on the math exam.

Percentile

A percentile is defined as the percentage of values that fall within a given range. The ranking system mostly employs percentiles. It is based on dividing the normal distribution of values. The percentile is denoted as xth, where x is an integer.

Assume a kid has an 80th percentile on a test with a total score of 150. By doing so, we can better understand the term percentile and realise that by achieving 150 on the exam, a student has outperformed 80% of the remaining class.

What is the Difference between Percentage and Percentile?

To get clarity on the concepts, let’s go through the Difference between Percentage and Percentile.

 Percentage Percentile A mathematical unit of measurement that shows the answer out of 100. A percentile is a value that is used to calculate the values of percentages below it. The percentage unit is denoted by %. The percentile unit is expressed as xth, for example, 30th. There are no quartiles. There are quartiles. A percentage can be expressed as a decimal or a ratio. A Percentile can’t be expressed in decimals or ratios. Percentages are not calculated using the rank of numbers. Percentages are not calculated using the rank of numbers. It is based on a single case. It is based on a comparison of one case to a number of cases. The normal distribution is not required. The normal distribution is used to calculate the percentile.

Fraction

A fraction, often known as a fractional number, is a number of the form p/q, where p and q are whole numbers and q is greater than zero (0). It represents a piece of a whole or any number of equal parts. It can also be described as a ratio of two integers, with the upper number (numerator) representing the number of equal parts into which the whole is divided and the lower number (denominator) representing the number of equal parts into which the whole is divided.

Some examples of fractional numbers are 3/5, 9/6, 8/4, and so on.

Rational Numbers

Rational numbers are ones with the form a/b, where a and b are integers and b is greater than zero (0). It can also be expressed as an integer ratio, that is, as a fraction of two integers with the numerator being the higher number and the denominator being the lower number. Some examples of rational numbers: 12/17,-2/17, 9/11, 9/-11 and 3/5.

Difference Between Fraction and Rational Numbers

 Rational Number Fraction A rational number is expressed in the form of p/q, where p and q are integers, and q≠0. For example, 4/5, -3/5, etc. A fraction is represented as a/b, where a and b are natural numbers and b≠0. For example, 11/2, 3/-4, etc. Not all rational numbers are fractions since negative numbers, like −5/7, don’t fit in the definition of fractions. Since fractions are always the ratio of positive integers, like 3/5, they are all rational numbers. A  rational number could be either positive or negative. For instance, 11/27, -13/15. A fraction can never be negative. For instance, 3/4.

#### Sneha Shukla

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