Write the following decimal as a percent. 0.567

To write the decimal $0.567$ as a percent, we follow a straightforward process. The word “percent” comes from the Latin “per centum,” meaning “per hundred.” Thus, converting a decimal to a percentage involves determining how many parts out of 100 the decimal represents. Here’s how to convert $0.567$ into a percentage:

Step-by-Step Explanation of the Conversion Process:

1. Understand the Basics:
   A decimal is a way of expressing a part of a whole. In decimal form, $0.567$ represents $567$ parts of a unit divided into $1000$ equal parts.
2. Multiply by 100:
   To convert a decimal to a percentage, multiply the decimal number by $100$. This operation essentially shifts the decimal point two places to the right. Mathematically:

   $$0.567\times 100=56.7$$

3. Add the Percent Symbol (%):
   After multiplying by $100$, attach the percent symbol (%) to the result. This indicates that the value is now expressed as a percentage. Therefore:

   $$0.567=56.7\%$$

4. Final Answer:
   The decimal $0.567$ is equivalent to $56.7\%$ when written as a percentage.

Why This Conversion Works:

The concept of percentages is rooted in proportions. When we say $56.7\%$, it means $56.7$ parts out of $100$. Multiplying the decimal by $100$ rescales it to fit the percentage system, which is based on a denominator of $100$.

Applications of Percentages:

Converting decimals like $0.567$ to percentages is a common practice in various fields. Let’s explore some scenarios where percentages are crucial:

1. Finance and Economics:

• Interest Rates: Banks often express interest rates as percentages. For example, an interest rate of $0.567$ as a decimal would be $56.7\%$ annually.
• Discounts and Markups: When shopping, discounts are given in percentages. If a product originally costs $100 and is discounted by $56.7\%$, the customer saves $56.70.

2. Statistics and Data Representation:

Percentages are used to represent proportions in surveys and reports. For instance, if $0.567$ of a survey population prefers a particular product, this translates to $56.7\%$ of the respondents.

3. Education and Grading:

Academic performance is often expressed as a percentage. For instance, if a student scores $0.567$ of the total marks, their percentage score would be $56.7\%$.

4. Daily Life and Comparisons:

Percentages simplify comparisons. For example, if a weather report indicates $0.567$ inches of rain compared to the annual average, expressing this as $56.7\%$ of the expected rainfall makes it easier to understand.

Common Misconceptions:

While converting decimals to percentages is straightforward, people sometimes make mistakes. Here are a few common errors:

1. Forgetting to Multiply by 100:
   Some may mistakenly leave the decimal unchanged, leading to incorrect interpretations.
2. Misplacing the Decimal Point:
   Moving the decimal point two places to the left or right can result in drastically different values.
3. Neglecting to Add the Percent Symbol:
   Without the % sign, the value remains a decimal and does not convey the intended meaning.

Advanced Considerations:

For individuals comfortable with mathematics, let’s delve into more complex scenarios:

Fractional Percentages:

Sometimes, percentages are represented as fractions for greater precision. For instance, $56.7\%$ could be expressed as 56710%56\frac{7}{10}\%56107​%.

Repeating Decimals:

If the decimal has repeating digits (e.g., $0.333\dots$), the conversion follows the same principle, but the percentage result may include a repeating decimal. For example, $0.333\dots$ becomes $33.333\dots \%$.

Large Numbers:

When dealing with large values, percentages provide clarity. For instance, $0.567$ of a billion dollars equates to $56.7\%$, or approximately $567 million.

Real-Life Example:

Imagine you’re managing a budget of $10,000. If $0.567$ of the budget is allocated to marketing, how much is that in percentage terms? Following the conversion process:

$$0.567\times 100=56.7\%$$

Thus, $56.7\%$ of the budget, or $5,670, goes toward marketing.

Practice Questions:

To solidify your understanding, try converting the following decimals into percentages:

1. $0.75$
2. $0.125$
3. $0.002$
4. $1.23$

Answers:

1. $75\%$
2. $12.5\%$
3. $0.2\%$
4. $123\%$

Conclusion:

Converting decimals like $0.567$ into percentages is an essential skill in mathematics with practical applications across various domains. The process is simple: multiply the decimal by $100$ and add the % symbol. By mastering this technique, you can easily interpret and communicate numerical data in a clear and meaningful way.