TLDR;
This Math Antics video introduces percentages, explaining that they are essentially fractions with a denominator of 100. It covers converting percentages to fractions and decimals, and vice versa. The video emphasizes the importance of understanding percentages for real-life applications and lays the groundwork for more advanced topics.
- Percentages are fractions with a denominator of 100.
- Percent literally means "per 100".
- Percentages can be easily converted to fractions and decimals.
- Moving the decimal point two places to the left converts a percentage to a decimal.
Introduction to Percentages [0:06]
The video introduces percentages as a crucial concept with numerous real-world applications, such as calculating sales tax, discounts, and understanding financial investments. It addresses the common question of when math concepts are used in real life, asserting that percentages are used very often. The video sets the stage for understanding percentages by revealing that a percent is a fraction.
Percents as Fractions [1:08]
A percent is a special type of fraction that always has 100 as its denominator. Because the denominator is always 100, it is represented by the percent sign (%). The term "percent" means "per 100," derived from "per" meaning "for each" and "cent" from the Latin word for 100. Examples provided include 3% (3/100), 10% (10/100), 25% (25/100), and 75% (75/100), illustrating how percentages can be directly converted into fractions with a denominator of 100.
Special Cases of Percents [2:57]
The video explores special cases of percentages, including 0%, which equals 0/100 or zero. 100% is equivalent to 100/100, representing one whole or 1. Numbers greater than 100, such as 126%, are also valid and equal 126/100, resulting in an improper fraction with a value greater than 1.
Converting Percents to Decimals [4:15]
Percentages are base-10 fractions, making it easy to rewrite them as decimal numbers. To convert a percentage to a decimal, move the decimal point two places to the left and remove the percent sign. For example, 35% becomes 0.35. If a number has only one digit, use a zero as a placeholder. For example, 4% becomes 0.04. Special cases like 0% convert to 0.00, and 100% converts to 1.00, which is the same as 1.
Converting Fractions and Decimals to Percents [7:48]
The video summarizes that a percent can be rewritten as a fraction with 100 as the bottom number or as a decimal. It also explains the reverse process: a fraction with 100 as the bottom number can be rewritten as a percent, and a decimal can be rewritten as a percent. For example, 12/100 is 12%, 80/100 is 80%, 0.10 is 10%, and 0.38 is 38%. Percentages are another way to write fractions and decimals.