7.2 Percent As A Decimal

7.2 Percent as a Decimal: A Comprehensive Guide

Understanding how to convert percentages to decimals is a fundamental skill in mathematics, with applications spanning various fields from finance and statistics to everyday calculations. This comprehensive guide delves into the conversion of 7.2 percent to its decimal equivalent, explaining the process step-by-step, providing illustrative examples, and addressing common queries. We'll explore the underlying principles and provide practical applications to solidify your understanding. This guide is designed for learners of all levels, from those just beginning to grasp percentages to those seeking a deeper understanding of the mathematical concepts involved.

Understanding Percentages and Decimals

Before diving into the conversion of 7.2 percent, let's establish a clear understanding of percentages and decimals. A percentage is a way of expressing a number as a fraction of 100. The symbol "%" represents "per hundred" or "out of 100". For example, 50% means 50 out of 100, which can be written as the fraction 50/100 or the decimal 0.50.

A decimal, on the other hand, is a way of expressing a number using a base-ten system. The decimal point separates the whole number part from the fractional part. For instance, 3.14 represents 3 whole units and 14 hundredths of a unit.

The relationship between percentages and decimals is direct: a percentage can always be expressed as a decimal, and vice-versa. This conversion is crucial for performing various calculations, particularly in areas like calculating interest rates, discounts, tax rates, and statistical analysis.

Converting 7.2 Percent to a Decimal: The Step-by-Step Process

Converting 7.2% to a decimal involves a straightforward process:

Step 1: Understand the meaning of percentage. Remember that the percentage symbol (%) signifies "per hundred." Therefore, 7.2% means 7.2 out of 100.

Step 2: Express the percentage as a fraction. This can be written as 7.2/100.

Step 3: Divide the numerator by the denominator. Performing the division 7.2 ÷ 100 gives us 0.072.

Therefore, 7.2% as a decimal is 0.072.

Illustrative Examples: Applying the Conversion

Let's explore some real-world scenarios where converting 7.2% to a decimal is useful:

Example 1: Calculating Sales Tax.

Suppose a state has a 7.2% sales tax. If you buy an item costing $50, the sales tax amount is calculated as follows:

• Convert the percentage to a decimal: 7.2% = 0.072
• Multiply the item's price by the decimal equivalent of the tax rate: $50 * 0.072 = $3.60
• The sales tax on the $50 item is $3.60.

Example 2: Calculating Interest Earned.

Imagine you have $1000 in a savings account that earns 7.2% annual interest. To calculate the interest earned in one year:

• Convert the percentage to a decimal: 7.2% = 0.072
• Multiply the principal amount by the decimal equivalent of the interest rate: $1000 * 0.072 = $72
• You would earn $72 in interest in one year.

Example 3: Calculating Percentage Decrease.

If a product's price decreases by 7.2%, and the original price was $200, you would calculate the new price as follows:

• Convert the percentage to a decimal: 7.2% = 0.072
• Calculate the amount of the decrease: $200 * 0.072 = $14.40
• Subtract the decrease from the original price: $200 - $14.40 = $185.60
• The new price of the product is $185.60

The Mathematical Principle Behind the Conversion

The conversion of percentages to decimals is based on the fundamental concept of expressing a value as a fraction of 100. When we write 7.2%, we're essentially saying 7.2 parts out of 100. To express this as a decimal, we divide the number of parts (7.2) by the total number of parts (100). This division is equivalent to moving the decimal point two places to the left.

Frequently Asked Questions (FAQ)

Q1: Why do we move the decimal point two places to the left when converting a percentage to a decimal?

A1: Moving the decimal point two places to the left is a shortcut method equivalent to dividing by 100. Since a percentage is a fraction out of 100, dividing by 100 effectively converts it to its decimal equivalent.

Q2: Can I convert percentages with decimal places, like 7.2%, directly to decimals?

A2: Yes, absolutely. The method remains the same: divide the percentage value by 100 or move the decimal point two places to the left.

Q3: What if I have a percentage greater than 100%?

A3: Percentages greater than 100% represent values greater than one whole unit. The conversion process is identical; simply divide by 100 (or move the decimal point two places to the left). For example, 125% becomes 1.25.

Q4: How do I convert a decimal back to a percentage?

A4: To convert a decimal back to a percentage, multiply the decimal by 100 and add the "%" symbol. For example, 0.072 * 100 = 7.2%, reversing the original conversion.

Q5: Are there any other methods to convert percentages to decimals besides division?

A5: While division by 100 is the most straightforward and widely understood method, you can also use equivalent fractions. For example, 7.2% can be expressed as 72/1000 which simplifies to 18/250 and so on; however, division by 100 is the most efficient for direct decimal conversion.

Conclusion: Mastering Percentage-to-Decimal Conversions

Mastering the conversion of percentages to decimals is a cornerstone of mathematical literacy. This skill is widely applicable in various contexts, from personal finance to advanced statistical analysis. By understanding the underlying principles and applying the straightforward steps outlined in this guide, you can confidently handle percentage-to-decimal conversions and utilize this knowledge effectively in diverse situations. Remember that the key lies in understanding that a percentage is simply a fraction out of 100, and conversion involves dividing by 100 or equivalently moving the decimal point two places to the left. Practice regularly and you'll become proficient in this essential mathematical skill. The conversion of 7.2% to 0.072 is just one example, and this same method applies to all percentage-to-decimal conversions.