Problem 57 - Elementary Algebra

Question

For exercises \(47-58\), rewrite the percent as a decimal number. $$ 0.6 \% $$

Step-by-Step Solution

Answer

0.006

Step 1 - Understand the Problem

The goal is to convert a percentage to a decimal. The percentage given is 0.6%.

Step 2 - Recall the Conversion Rule

To convert a percentage to a decimal, divide the percentage by 100. This helps to shift the decimal point two places to the left.

Step 3 - Apply the Conversion

Write the percentage as a fraction over 100. For 0.6%, this becomes \(\frac{0.6}{100}\).

Step 4 - Perform the Division

Calculate the division: \(\frac{0.6}{100} = 0.006\).

Step 5 - Write the Answer

The decimal equivalent of 0.6% is 0.006.

Key Concepts

Converting Percentages

Understanding how to convert percentages into decimals is a crucial concept in mathematics. Here, we're focusing on converting a percentage, like 0.6%, into a decimal number. The key thing to remember is that percentages represent parts out of 100. So, when you convert a percentage to a decimal, you're simply expressing that percentage as a fraction of 100. Let's break it down into simpler steps:

• Identify the percentage you need to convert. In this case, it's 0.6%.
• To convert, divide the percentage by 100. This essentially moves the decimal point two places to the left.
• For instance, \(\frac{0.6\text\bf{\text{\tiny{\tiny{\text{\tiny{\tiny{\text{\tiny{\tiny{\text{\tiny{\tiny{\text{\tiny{\tiny{\text{\tiny{\tiny{\fractions{\fractions{\fractions{\fractions}}\{\text{\tiny{\tiny{\tiny{\tiny{\fractions} \text{\tiny{\fractions{\{\tiny{\tiny{\tiny{\tiny{\fractions{\fractions{\fractions\textbf{\frac{0.6}{100}= 0.006}}}}}}}}}}}}}}\).
  
• This results in the decimal representation of the percentage you started with.

Converting percentages is straightforward once you understand this basic principle.

Decimal Representation

Decimals are a way to represent fractions and percentages in a base-10 system, which is the system we use for most of our daily calculations. They use a decimal point to separate the whole number part from the fractional part.

• When you have a percentage, it's beneficial to remember that it's a fraction of 100.
• By dividing by 100, you move the decimal point two places to the left if you have a whole number percentage.
• For a percentage like 0.6%, you shift the decimal in 0.6 two places to the left, resulting in 0.006.

This decimal represents the same value as the percentage but in a different form, which can be more useful for certain mathematical operations.

Basic Arithmetic Operations

Arithmetic operations are the foundation of most mathematical tasks. Being comfortable with converting percentages to decimals will make these operations easier to handle. Here's why:

• Adding, subtracting, multiplying, or dividing with decimals is often simpler than working directly with percentages.
• For example, multiplying a number by a percentage is easier when you use the decimal form of that percentage.
• Knowing that 0.6% converts to 0.006 allows you to multiply directly by the decimal.

Next time you have a percentage, remember how easy it is to convert it to a decimal to simplify your calculations.