Problem 25 - Prealgebra

Question

Change each decimal to a percent. $$0.45$$

Step-by-Step Solution

Answer

0.45 as a percent is 45%.

Step 1: Understand the Conversion

A decimal can be converted to a percentage by multiplying it by 100. This is because 'percent' means 'per hundred,' so we want to see how many 'per 100' the decimal represents.

Step 2: Multiply the Decimal by 100

Take the decimal 0.45 and multiply it by 100. This will convert the decimal to a percentage.\[0.45 \times 100 = 45\]

Step 3: Add the Percent Symbol

Once you have the product from the previous step, add the percent symbol (%) to indicate the result is a percentage. From Step 2, the number we have is 45, so it becomes 45%.

Key Concepts

Percentages

Percentages are a way to express numbers as parts of 100. They are a useful way to compare ratios, understand changes, or present statistics in a familiar manner.
The word 'percent' comes from the Latin 'per centum,' which means 'by the hundred.' Essentially, when we talk about percentages, we express a number as a fraction of 100. This is why percentages are often simpler to understand than fractions or decimals, especially when comparing quantities.
For example, if you have a score of 90 out of 100 on a test, it corresponds to a 90% score. This implies if the total possible were 100, 90 parts out of it were achieved. Therefore, percentages play a crucial role in understanding proportions and ratios in everyday contexts.

Mathematical Conversion

Mathematical conversion between decimals and percentages is a fundamental skill in arithmetic. This conversion is straightforward once you understand the principle behind it.
The process involves multiplying the decimal number by 100 to shift its decimal point two places to the right. By doing this operation, you effectively convert the decimal into a form that compares it to a number out of 100, making it a percentage.
For example, if you start with the decimal 0.45 and multiply it by 100, you shift the decimal places: 0.45 becomes 45. In this context, 0.45 as a percentage equals 45% because it represents 45 parts of 100. Converting decimals to percentages is a handy mathematical conversion, useful in finance, science, and everyday calculations.

Basic Arithmetic

Basic arithmetic involves operations like multiplication, which is at the core of converting decimals to percentages. Specifically, the operation carried out in the conversion is multiplication by 100.
In arithmetic, multiplying a number by 100 simply involves an internalized trick: each digit is moved two places to the left in a number, effectively scaling the number up to a larger comparable whole. This makes the decimal align naturally into a percentage format.

• Start with any decimal: for instance, 0.45.
• Multiply it by 100: the decimal moves two places to the left—resulting in 45.
• End with a percentage: add the % symbol to mark the conversion: 45%.

Understanding this simple arithmetic transformation aids in numerous fields, ensuring precise calculation and clear expression of data.