Percentages are a fundamental concept in mathematics and everyday life. They represent A Special Ratio That Compares A Number To 100, using the symbol %. The term “percent” literally means “per hundred,” making it easy to understand and apply in various situations.
Defining and Representing Percentages
A percentage is a way of expressing a proportion or a fraction as a part of 100. For example, if 35 out of 100 marbles are red, then 35% of the marbles are red. Similarly, using 25 out of 100 postage stamps means you’ve used 25% of your stamps.
Percentages can be easily represented as fractions and decimals. Since a percentage is based on 100, any percentage can be written as a fraction with a denominator of 100. For instance, 35% is equivalent to the fraction 35/100. This fraction can be further simplified to 7/20 by dividing both the numerator and the denominator by their greatest common factor, which is 5.
Furthermore, percentages can be converted to decimals. 35/100 can be written as the decimal 0.35. This highlights the direct relationship between percentages, fractions, and decimals.
Converting Between Decimals and Percentages
Converting a decimal to a percent involves moving the decimal point two places to the right and adding the percent symbol. For example, the decimal 0.8 is equivalent to 80%. This is because 0.8 can be expressed as the fraction 8/10, which is equal to 80/100, or 80%.
Conversely, to convert a percentage to a decimal, the process is reversed. Drop the percent symbol and move the decimal point two places to the left. For instance, 12.5% becomes 0.125. A helpful mnemonic device to remember the direction of the decimal shift is “Dr. Pepper” (DP). When moving from a Decimal to a Percent, move the decimal point two places to the right. When moving from a Percent to a Decimal, drop the percent sign and move the decimal two places to the left.
Working with Fractions and Percentages
Converting fractions to percentages can be done by first converting the fraction to a decimal through division and then converting the decimal to a percentage as described above. For example, the fraction 1/3 is equal to the repeating decimal 0.333…, which is approximately 33.33%.
Percentages are also used to represent parts of a whole. If 28% of a class failed a quiz, then the remaining 72% (100% – 28%) passed. This 72% can be represented as the fraction 72/100, which simplifies to 18/25.
Conclusion
Understanding percentages as a special ratio compared to 100 provides a crucial foundation for numerous mathematical concepts and real-world applications. The ability to convert between percentages, decimals, and fractions is essential for interpreting data, calculating proportions, and making informed decisions in various contexts. From understanding discounts and interest rates to analyzing statistics and survey results, percentages play a vital role in our daily lives.
