Question

PERCENTS AS DECIMALS Write the percent as a decimal. $$ 255 \% $$

Short answer

255% as a decimal is 2.55.

Step-by-step solution

Identify the notion of percent

Percent means 'per hundred'. So, a percentage is a way of expressing a number as a fraction of 100.

Convert the percentage to a decimal

To convert the percentage to a decimal, move the decimal point two places to the left. For example, 25% converted to a decimal would be 0.25. To convert 255% into a decimal, move the decimal point two places left, and you get 2.55.

Key concepts

Percentages

The use of percentages is a fundamental concept in mathematics, often applied in various fields like finance, statistics, and everyday calculations. A percentage represents a portion of a whole and is typically understood as parts per hundred. This means that when we talk about percentages, we are referring to how many parts out of a hundred make up a certain quantity. For instance, if you score 90% on a test, it implies you got 90 questions correct out of a possible 100.

To visualize percentages, imagine cutting a cake into 100 equal pieces. Each slice represents 1%. Therefore, if you eat 25 pieces, you have eaten 25% of the cake. It's a way to standardize comparisons, such as the rate of growth, discounts on products, or the proportion of a population that favors a particular opinion. Understanding percentages allows students to interpret and communicate quantitative information effectively in real-world situations.

Decimal Conversion

Converting percentages to decimals is a straightforward process, but one that's important to understand, as decimals are easier to work with in calculations. To manage this conversion, you need to move the decimal point two places to the left. The reason is that 'percent' means 'per hundred' or 'out of hundred', so you are essentially dividing the percentage by 100 to find its decimal form.

Let's consider the number 50%. To convert this to a decimal, we think of 50 percent as 50 per 100, which can also be written as the fraction \(\frac{50}{100}\). When we divide 50 by 100, the decimal is 0.50. It is also helpful to remember that the decimal point in a whole number is at the end, so for 50 or 50., moving the decimal point two places to the left gives us 0.50.

Mathematical Notation

Mathematical notation is the system of symbols and abbreviations used to express mathematical concepts and operations succinctly. It is a language that enables mathematicians and students to write complex ideas elegantly and precisely. In the context of percentages and decimals, we use symbols such as \(\%\) for percent and a period (.) to indicate the decimal point.

Understanding how to read and write in this notation is crucial for competency in math. For example, the percentage symbol after a number communicates that this number is a rate per 100, and appropriately placing and moving the decimal point when converting percentages to decimals is an application of this notation. Proper usage of mathematical notation ensures clarity in solving problems and makes your mathematical thinking visible to others.

Fractions

Fractions are yet another way to express parts of a whole and are deeply connected to percentages and decimals. A fraction consists of a numerator (the top number), which represents the number of parts you have, and a denominator (the bottom number), which denotes how many parts make up the whole.

Percentages can be thought of as fractions with a denominator of 100 because 'per cent' means 'per hundred'. So, when you have a percentage, you already have a fraction with a denominator of 100. To convert this percentage to a decimal, which is another form of a fraction, we simply divide the numerator by the denominator. For instance, the percentage 75% is the fraction \(\frac{75}{100}\), which is equivalent to the decimal 0.75 when the division is performed. Recognizing the relationship between fractions, decimals, and percentages is essential for grasping the underlying unity of these mathematical concepts.