Expressing the New Value as a Decimal

Oct 13, 2025 by recoveryshake.com 145 views

Introduction

When it comes to real estate, the value of a house can fluctuate over time due to various factors such as market trends, economic conditions, and physical changes to the property. In this scenario, we are given a house valued at $\$377,000$ and are asked to find its new value after a decrease of $18\%$ . This problem requires us to apply mathematical concepts to calculate the new value of the house in terms of its original value.

Understanding the Problem

To solve this problem, we need to understand the concept of percentage decrease. A percentage decrease represents the amount by which a quantity decreases as a percentage of its original value. In this case, the house's value decreases by $18\%$ , which means that the new value is $82\%$ of the original value.

Calculating the New Value

Let's denote the original value of the house as $x$ . We are given that the house's value decreases by $18\%$ , so the new value can be represented as $0.82x$ . This is because $82\%$ of the original value is equal to $0.82x$ .

Expressing the New Value as a Decimal

To express the new value as a decimal, we need to multiply the original value by $0.82$ . This will give us the new value in terms of the old value.

Solution

The new value of the house can be expressed as:

\text{New Value} = 0.82 \times \text{Original Value}

Substituting the original value of $\$377,000$ , we get:

\text{New Value} = 0.82 \times 377,000 = 309,260

Therefore, the new value of the house is $\$309,260$ .

Conclusion

In this problem, we applied mathematical concepts to calculate the new value of a house after a decrease of $18\%$ . We expressed the new value as a decimal by multiplying the original value by $0.82$ . This demonstrates the importance of understanding percentage decrease and its application in real-world scenarios.

Real-World Applications

The concept of percentage decrease has numerous real-world applications, including:

Finance: Understanding percentage decrease is crucial in finance, as it helps investors and financial analysts calculate the impact of market fluctuations on investments.
Economics: Percentage decrease is used to analyze economic trends and forecast future economic conditions.
Business: Businesses use percentage decrease to evaluate the effectiveness of marketing campaigns and adjust their strategies accordingly.

Common Mistakes to Avoid

When working with percentage decrease, it's essential to avoid common mistakes such as:

Misinterpreting percentage decrease: Percentage decrease represents the amount by which a quantity decreases as a percentage of its original value.
Not considering the original value: When calculating the new value, it's crucial to consider the original value and apply the percentage decrease accordingly.

Tips and Tricks

To master percentage decrease, follow these tips and tricks:

Practice, practice, practice: The more you practice calculating percentage decrease, the more comfortable you'll become with the concept.
Use real-world examples: Apply percentage decrease to real-world scenarios to better understand its practical applications.
Check your work: Double-check your calculations to ensure accuracy and avoid common mistakes.

Q&A: Frequently Asked Questions

Q: What is percentage decrease?

A: Percentage decrease represents the amount by which a quantity decreases as a percentage of its original value. In this case, the house's value decreases by $18\%$ , which means that the new value is $82\%$ of the original value.

Q: How do I calculate the new value of a house after a decrease of $18\%$ ?

A: To calculate the new value, multiply the original value by $0.82$ . This will give you the new value in terms of the old value.

Q: What is the formula for calculating the new value?

A: The formula for calculating the new value is:

\text{New Value} = 0.82 \times \text{Original Value}

Q: Can I use a calculator to calculate the new value?

A: Yes, you can use a calculator to calculate the new value. Simply multiply the original value by $0.82$ and you'll get the new value.

Q: What if I want to find the original value of a house after a decrease of $18\%$ ?

A: To find the original value, divide the new value by $0.82$ . This will give you the original value in terms of the new value.

Q: How do I express the new value as a decimal?

A: To express the new value as a decimal, multiply the original value by $0.82$ . This will give you the new value in decimal form.

Q: Can I use percentage decrease to calculate the new value of a house after a decrease of $25\%$ ?

A: Yes, you can use percentage decrease to calculate the new value of a house after a decrease of $25\%$ . Simply multiply the original value by $0.75$ (since $100\% - 25\% = 75\%$ ) and you'll get the new value.

Q: What if I want to find the percentage decrease of a house's value?

A: To find the percentage decrease, subtract the new value from the original value and divide by the original value. This will give you the percentage decrease as a decimal.

Q: Can I use percentage decrease to calculate the new value of a house after a decrease of $10\%$ ?

A: Yes, you can use percentage decrease to calculate the new value of a house after a decrease of $10\%$ . Simply multiply the original value by $0.90$ (since $100\% - 10\% = 90\%$ ) and you'll get the new value.

Q: What if I want to find the original value of a house after a decrease of $10\%$ ?

A: To find the original value, divide the new value by $0.90$ . This will give you the original value in terms of the new value.