Write the following decimal as a percent. 0.084

Understand What a Percent Is

A percent is a way of expressing a number as a fraction of 100. The word “percent” comes from the Latin phrase per centum, meaning “by the hundred.” Therefore, when you convert a decimal to a percent, you are essentially expressing the decimal value as a part of 100.

How to Convert a Decimal to a Percent

To convert any decimal number to a percent, the rule is simple:

1. Multiply the decimal by 100.
2. Add the percent symbol (%).

Convert 0.084 to a Percent

Let’s apply this rule to convert the decimal 0.084 into a percent.

1. Multiply the decimal 0.084 by 100:

$$0.084\times 100=8.4$$

2. Add the percent symbol to the result:

$$8.4\%$$

So, the decimal 0.084 is equivalent to 8.4%.

Why This Works

When you multiply a decimal by 100, you are essentially shifting the decimal point two places to the right. This is because multiplying by 100 increases the value by two orders of magnitude. For example:

• The decimal 0.1 becomes 10%.
• The decimal 0.01 becomes 1%.

In the case of 0.084, multiplying by 100 moves the decimal point two places to the right, turning it into 8.4.

Decimal and Percent Relationship

The relationship between decimals and percents is consistent across all numbers. Here are a few more examples to illustrate:

• 0.5 as a percent:
  Multiply 0.5 by 100:

  $$0.5\times 100=50$$Result: 50%

• 0.25 as a percent:
  Multiply 0.25 by 100:

  $$0.25\times 100=25$$Result: 25%

• 0.002 as a percent:
  Multiply 0.002 by 100:

  $$0.002\times 100=0.2$$Result: 0.2%

Application of Percentages in Real Life

Understanding how to convert decimals to percentages is not just useful for academic purposes; it has practical applications in various real-life situations, such as:

• Financial Calculations: Percentages are used to calculate interest rates, sales tax, and tips. For example, a 5% sales tax on a $100 item would cost an additional $5.
• Statistics: Percentages help to express data and probabilities. For example, if a survey shows that 30 out of 100 people prefer a certain brand, this can be expressed as 30%.
• Discounts and Promotions: Retail stores often advertise discounts in percentages. If an item originally costs $200 and is on sale for 25% off, the new price would be calculated by subtracting 25% from the original price.

Common Mistakes to Avoid When Converting Decimals to Percentages

While the conversion process is relatively simple, there are some common errors that people often make when converting decimals to percentages:

• Forgetting to multiply by 100: This is the most common mistake. Some people might simply add the percent sign without multiplying by 100 first, leading to an incorrect result.
• Misplacing the Decimal Point: When multiplying a decimal by 100, it’s important to shift the decimal point two places to the right. For example, multiplying 0.084 by 100 correctly gives 8.4%, but if you accidentally shift the decimal point only one place, you would get 0.84%, which is incorrect.

Converting Percents to Decimals

Just as we can convert decimals to percentages, we can also go in the opposite direction—convert percentages back to decimals. To convert a percentage to a decimal, divide the percentage by 100 or simply move the decimal point two places to the left.

For example:

• 8.4% to decimal:
  Divide 8.4 by 100 or move the decimal two places to the left: $$8.4÷100=0.084$$ Result: 0.084

Summary

In summary, to convert the decimal 0.084 to a percent, you multiply the decimal by 100, which results in 8.4%. This process is applicable to any decimal number and is an essential mathematical skill for interpreting and using percentages in various contexts. Whether you’re calculating interest rates, interpreting statistical data, or working out sales tax, understanding how to convert decimals to percentages is a fundamental concept in mathematics and everyday life.

By following the simple steps outlined—multiplying by 100 and adding the percent symbol—you can easily convert any decimal into its corresponding percentage.

Further Exploration of Decimal to Percent Conversion

While the basic rule of multiplying a decimal by 100 works for most situations, there are cases where you might need to handle decimals that involve more complex numbers or additional rules. Let’s look at some of those cases:

Decimal Values Less Than One

So far, we’ve been working with decimals smaller than 1. The same principle applies to any decimal value, no matter how small. For instance:

• 0.003 to a percent:
  Multiply 0.003 by 100:

  $$0.003\times 100=0.3$$Result: 0.3%

• 0.0005 to a percent:
  Multiply 0.0005 by 100:

  $$0.0005\times 100=0.05$$Result: 0.05%

As you can see, even decimals smaller than 1 can be converted to percentages, and they result in very small percentages.

Decimal Values Greater Than One

What if the decimal number is greater than 1? For example, consider 1.25. This is still a valid decimal, and the same rule applies. When converting decimals greater than one into a percentage, the number gets larger after multiplying by 100.

• 1.25 to a percent:
  Multiply 1.25 by 100: $$1.25\times 100=125$$ Result: 125%

This indicates that 1.25 is 125% of something. It’s helpful to note that numbers greater than 1 can be converted to percentages greater than 100%.

More Examples of Decimal to Percent Conversion

Here are several more examples to help solidify the concept of converting decimals into percentages.

1. Decimal: 0.6
   Multiply 0.6 by 100:

   $$0.6\times 100=60$$Result: 60%

2. Decimal: 0.09
   Multiply 0.09 by 100:

   $$0.09\times 100=9$$Result: 9%

3. Decimal: 1.75
   Multiply 1.75 by 100:

   $$1.75\times 100=175$$Result: 175%

4. Decimal: 0.004
   Multiply 0.004 by 100:

   $$0.004\times 100=0.4$$Result: 0.4%

Applications of Percentages in Real Life

Percentages are used daily in a wide range of fields. Let’s take a closer look at some practical examples where understanding the conversion from decimals to percentages is essential.

Financial Calculations

In finance, percentages are used frequently to calculate interest rates, investment returns, and other important metrics.

• Interest Rates: Suppose you have a savings account that offers an annual interest rate of 0.02 (or 2%). To understand the interest you’d earn, you would multiply this decimal by 100 to convert it to a percentage.

  $$0.02\times 100=2\%$$So, the interest rate is 2% per year.

• Discounts: During sales events, stores often offer discounts in percentages. If a store advertises a 30% discount, and the original price of a jacket is $100, then you would subtract 30% of $100 to calculate the final price.

  $$30\%\times 100=30\text{ dollars}$$Final price = $100 – $30 = $70.

Statistics and Data Analysis

In statistics, percentages are widely used to represent data. For example, if a poll shows that 50 out of 200 participants prefer a particular product, you would convert the fraction to a percentage to understand it better.

• Fraction to Percentage:
  The fraction is 50200\frac{50}{200}20050​, and to convert this into a percentage: 50200=0.25(Decimal form)\frac{50}{200} = 0.25 \quad \text{(Decimal form)}20050​=0.25(Decimal form) Multiply by 100: $$0.25\times 100=25\%$$ So, 25% of the participants prefer that product.

Cooking and Recipes

Percentages are also helpful in cooking, especially when adjusting portions or recipes. If a recipe calls for 0.5 cups of flour and you want to double the recipe, you’ll need to increase the flour by 100%, which is the same as multiplying the original amount by 2.

For example, if you use 0.5 cups of flour and need to increase the amount by 100%, the total amount of flour required will be:

$$0.5\times 2=1\text{ cup}$$

This concept helps in meal planning and preparation.

Understanding Large Numbers with Percentages

In certain fields, you may deal with percentages that involve large numbers. For example, in the stock market or economics, a small change in a large number can have a significant impact. Understanding how to interpret these percentages can make a big difference.

Example: Stock Market Change

Let’s say a company’s stock price rises from $20 to $25. To find the percentage increase:

1. Calculate the difference in the prices:

   $$25-20=5$$

2. Divide the difference by the original price:

   520=0.25\frac{5}{20} = 0.25205​=0.25

3. Convert the decimal into a percentage:

   $$0.25\times 100=25\%$$

So, the stock price increased by 25%.

Example: World Population Growth

Consider the global population increasing from 7 billion to 7.4 billion. To calculate the percentage increase:

1. Calculate the difference in population:

   $$7.4\text{billion}-7\text{billion}=0.4\text{billion}$$

2. Divide the difference by the original population:

   0.47≈0.0571\frac{0.4}{7} \approx 0.057170.4​≈0.0571

3. Convert the decimal into a percentage:

   $$0.0571\times 100\approx 5.71\%$$

So, the population increased by approximately 5.71%.

Decimal and Percent in Science and Engineering

In scientific fields, decimals and percentages are often used to represent concentrations, measurements, and even probabilities in experiments.

• Concentration: In chemistry, the concentration of a solution is often expressed as a percentage. For example, a solution that is 0.25% salt means that 0.25 grams of salt are dissolved in 100 grams of solution.
• Error Rates: In engineering, the error rate of a calculation or measurement is often expressed as a percentage. A measurement error of 0.05 might be expressed as 5% to indicate how far off the measurement was compared to the expected value.

Conclusion

In conclusion, converting decimals to percentages is a simple and powerful mathematical tool that can be applied in a wide range of practical situations. Whether you’re working in finance, statistics, cooking, or analyzing scientific data, understanding how to switch between decimals and percentages is essential for accurate interpretation and communication of information.

By multiplying a decimal by 100, we can quickly transform any decimal into its percentage equivalent, allowing for easy comparison and understanding. With this knowledge, you’re better equipped to handle everyday tasks, from calculating discounts to interpreting data in a variety of fields.