Problem 20 - Elementary Algebra

Question

For the following problems, convert each decimal to a percent. $$ 21.26 $$

Step-by-Step Solution

Answer

Question: Convert the decimal number 21.26 into a percentage. Answer: 2126%

Step 1: Identify the decimal

The decimal number given in the problem is 21.26.

Step 2: Multiply the decimal by 100

To convert the decimal to a percentage, you need to multiply it by 100. So, we have: $$(21.26) \times (100)$$

Step 3: Calculate the product

Now, we need to perform the multiplication: $$(21.26) \times (100) = 2126$$

Step 4: Add the percent symbol

The last step is to add the percent symbol (%) to the result of the multiplication. So, the final answer is: $$2126 \%$$ Hence, the decimal 21.26 is equivalent to 2126% as a percentage.

Key Concepts

Decimal to Percent Conversion

When we talk about converting a decimal to a percent, we're simply looking to express the decimal number as a part of 100. This is because 'percent' means 'per 100'. For instance, if we're given a decimal like 0.75, we can understand it as 75 parts out of a 100, or simply 75%.

The process is quite straightforward. If a decimal is given, such as the number 21.26 from the exercise, we interpret this number as '21.26 per 1'. But to convert it into a percentage, we need to adjust it to 'per 100'. This results in a simple mathematical operation, which involves moving the decimal point two places to the right. This move is the equivalent of multiplying by 100, which leads us right into our next concept.

Multiplication by 100

Why do we multiply by 100 when converting a decimal to a percent? Because percentages are essentially a fraction with a denominator of 100. Multiplying by 100 elevates the decimal value to its equivalent whole number in relation to 100.

To illustrate, for our example with the decimal 21.26, when we multiply by 100, we are essentially performing the operation \(21.26 \times 100\). It places the decimal point two places to the right, making it 2126, which tells us that 21.26 is the same as 2126 per 100. Remember, multiplying by 100 is the same as shifting the decimal point two places to the right for decimals. This method is a critical step in the conversion process and helps visualize how much of a 'whole' the decimal represents in percentage terms.

Placing the Percent Symbol

After performing the multiplication by 100, the last step in the conversion is to place the percent symbol (\(%\)) at the end of the number. This symbol is vital as it transforms the number from a simple numeric value into a percentage, explicitly indicating that the number is a particular number of parts out of 100.

In our textbook exercise, the number 2126 from the multiplication result now becomes 2126%. Placement of the percent symbol is essential to differentiate between '2126' as a quantity and '2126%' as a proportion of a whole denoted by 100. It is the universally recognized sign that the number preceding it is a percentage, allowing for immediate understanding that it relates to a part of a whole, based on a scale of 100.