Percentages, Fractions, and Decimals

Percentages, Fractions and Decimals are connected with each other.

We often see the phrases like

  • up to 75% off on all items
  • 90% housing loan with low-interest rates
  • 10% to 50% discount advertisements

These are some examples of percentages.

Suppose, there are 200 students in a college. Let 80 students remain in college to participate in college extra-curricular activities (ECA). The fraction of students participated in college ECA can be written as $\frac{80}{100}$, or $\frac{40}{100}$, or $\frac{2}{5}$. We can read it as 80 out of 200 students participated in ECA (or 2 out of 5 participated in ECA). Multiplying this fraction with 100 will convert the fraction to percentages. Therefore, 40% of the students participated in ECA.

By percent means that for every hundred or out of every hundred.

Therefore, a percentage is a fraction whose denominator is always 100. Therefore, a percentage can be converted to a fraction by dividing it by 100. Alternatively, one can change a fraction or a decimal to a percentage by multiplying it by 100. The following figure is about the conversion cycle of percentage to fraction or decimal and vise versa.

Percentages, Fractions, and Decimals

Real-life Example of Percentages, Fractions, and Decimals

Suppose, you are told that 70% of the students in a class of 50 passed a Mathematics test. How many of them failed?

Number of Students passed the Mathematics test = 70% of 50 = $\frac{70}{100}\times 50 = 35$

Number of students who failed the Mathematics test = $50 – 35 = 15$.

Number of students who failed can be found in an alternative way

\[(100-70)\%\times 50 = \frac{30}{100}\times 50 = 15\]

Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, Python, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

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