Problem 70 - Algebra A Combined Function

Question

Write each percent as \(a\) decimal. $$ 0.6 \% $$

Step-by-Step Solution

Answer

0.6% as a decimal is 0.006.

Step 1: Understand the Percent Definition

Percent means 'per hundred'. This means 0.6% is 0.6 per 100.

Step 2: Convert Percent to Decimal

To convert percent to a decimal, divide by 100. For 0.6%, divide 0.6 by 100: \[ 0.6 \div 100 = 0.006 \]

Step 3: Confirm the Conversion

By checking, you multiply the decimal by 100 to see if it equals the original percent. \[ 0.006 \times 100 = 0.6 \] Confirms that the conversion is correct.

Key Concepts

Percent Definition

A percent is a way to express a number as a part of 100. The word 'percent' comes from the Latin "per centum," meaning "by the hundred." When you see a percentage like 0.6%, it means 0.6 out of 100 or 0.6 per hundred.

Understanding the idea of percent is essential in many areas, such as finance, statistics, and everyday mathematics. It helps describe proportional relationships in a more intuitive and standardized form. In essence, a percentage tells you how much of a part you are dealing with in comparison to the whole, which is always 100 in this context. This understanding sets the stage for converting percentages into decimal numbers.

Decimal Conversion

Converting a percent to a decimal is straightforward once you know the process. The goal is to shift from expressing a number as parts of a hundred to expressing it in terms of whole or partial units.

To convert a percentage to a decimal:

• Take the percentage value, such as 0.6%.
• Remove the percentage sign.
• Divide the number by 100, which is the mathematical action that achieves the conversion.

For our example, dividing 0.6 by 100 gives us 0.006. This result is simply the decimal equivalent of the percentage initially provided. Remember, moving from percent to decimal changes the way we visually interpret and use the number but not its intrinsic value.

Mathematical Division

Mathematical division is an arithmetic operation that is crucial for converting percentages to decimals. It involves distributing a number into a specified number of equal parts.

In the context of percent to decimal conversion, division by 100 is used to transform the percentage value into a decimal format. Here's a step-by-step breakdown of our earlier example:

• Start with the percentage: 0.6%.
• The division operation is: 0.6 divided by 100.
• Perform the division to get the result: 0.006.

This process sights a simple concept: in arithmetic, dividing by 100 is equivalent to moving the decimal point two places to the left. It's a practical technique because it simplifies calculations and fosters better understanding in how percentages relate to decimals. This division serves as a confirmation step, anchoring the conversion process firmly in mathematical reasoning.