Express The First Quantity As A Percentage Of The Second;;(e) 30cm, 1.5m . (f) 6 Hours, 4 Days.​

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Introduction

In mathematics, expressing one quantity as a percentage of another is a fundamental concept that helps us understand the relationship between two values. This skill is essential in various fields, including finance, science, and engineering. In this article, we will explore how to express the first quantity as a percentage of the second, using real-world examples to illustrate the concept.

Expressing Quantities as Percentages

To express one quantity as a percentage of another, we need to follow a simple formula:

Percentage = (First quantity / Second quantity) x 100

Example (e): Expressing 30cm as a Percentage of 1.5m

Let's start with the first example: expressing 30cm as a percentage of 1.5m.

  • Step 1: Convert both quantities to the same unit. In this case, we will convert 1.5m to centimeters.
  • Step 2: Calculate the ratio of the first quantity to the second quantity.
  • Step 3: Multiply the ratio by 100 to get the percentage.

Here's the calculation:

1.5m = 150cm (converting 1.5m to centimeters) 30cm / 150cm = 0.2 0.2 x 100 = 20%

Therefore, 30cm is equal to 20% of 1.5m.

Example (f): Expressing 6 hours as a Percentage of 4 days

Now, let's move on to the second example: expressing 6 hours as a percentage of 4 days.

  • Step 1: Convert both quantities to the same unit. In this case, we will convert 4 days to hours.
  • Step 2: Calculate the ratio of the first quantity to the second quantity.
  • Step 3: Multiply the ratio by 100 to get the percentage.

Here's the calculation:

4 days = 96 hours (converting 4 days to hours) 6 hours / 96 hours = 0.0625 0.0625 x 100 = 6.25%

Therefore, 6 hours is equal to 6.25% of 4 days.

Real-World Applications

Expressing quantities as percentages has numerous real-world applications. Here are a few examples:

  • Finance: When investing in stocks or bonds, it's essential to understand the percentage return on investment. For instance, if you invest $100 in a stock that increases by 20%, you will have a total of $120.
  • Science: In scientific experiments, researchers often need to express the percentage of a substance in a mixture. For example, if a solution contains 30% sugar, it means that 30 grams of sugar are present in every 100 grams of the solution.
  • Engineering: In engineering, expressing quantities as percentages is crucial in designing and optimizing systems. For instance, if a machine has a 20% efficiency rate, it means that 20% of the input energy is converted into useful work.

Conclusion

Expressing quantities as percentages is a fundamental concept in mathematics that has numerous real-world applications. By following the simple formula and using real-world examples, we can understand the relationship between two values and make informed decisions in various fields. Whether you're a student, a professional, or simply someone interested in mathematics, this skill is essential to master.

Tips and Tricks

Here are some tips and tricks to help you express quantities as percentages:

  • Use a calculator: When working with large numbers, it's easy to make mistakes. Use a calculator to ensure accuracy.
  • Check your units: Make sure that both quantities are in the same unit before calculating the percentage.
  • Round your answer: In most cases, you don't need to express the percentage to the exact decimal place. Round your answer to the nearest whole number or two decimal places.

By following these tips and tricks, you'll become proficient in expressing quantities as percentages and be able to apply this skill in various real-world scenarios.

Practice Problems

Here are some practice problems to help you reinforce your understanding of expressing quantities as percentages:

  • Express 25cm as a percentage of 2m.
  • Express 8 hours as a percentage of 3 days.
  • Express 40% of 150 as a percentage of 200.

Try solving these problems on your own, and then check your answers with the solutions provided below.

Solutions

  • 25cm is equal to 16.67% of 2m.
  • 8 hours is equal to 11.11% of 3 days.
  • 40% of 150 is equal to 60% of 200.

Q&A: Expressing Quantities as Percentages

Q: What is the formula for expressing one quantity as a percentage of another?

A: The formula for expressing one quantity as a percentage of another is:

Percentage = (First quantity / Second quantity) x 100

Q: How do I convert quantities to the same unit before calculating the percentage?

A: To convert quantities to the same unit, you can use the following steps:

  • Step 1: Identify the units of the two quantities.
  • Step 2: Determine the conversion factor between the two units.
  • Step 3: Multiply the first quantity by the conversion factor to get the equivalent quantity in the second unit.

Q: What is the difference between a percentage and a ratio?

A: A percentage is a way of expressing a part of a whole as a fraction of 100. A ratio, on the other hand, is a comparison of two or more quantities. While a percentage is a way of expressing a ratio as a fraction of 100, a ratio can be expressed as a percentage by multiplying it by 100.

Q: How do I express a percentage as a decimal?

A: To express a percentage as a decimal, you can divide the percentage by 100. For example, 25% can be expressed as 0.25.

Q: Can I express a decimal as a percentage?

A: Yes, you can express a decimal as a percentage by multiplying it by 100. For example, 0.25 can be expressed as 25%.

Q: What is the difference between a percentage increase and a percentage decrease?

A: A percentage increase is a way of expressing a change in a quantity as a fraction of the original quantity. A percentage decrease, on the other hand, is a way of expressing a reduction in a quantity as a fraction of the original quantity.

Q: How do I calculate a percentage increase or decrease?

A: To calculate a percentage increase or decrease, you can use the following formula:

Percentage change = (New quantity - Original quantity) / Original quantity x 100

Q: Can I use a calculator to calculate percentages?

A: Yes, you can use a calculator to calculate percentages. In fact, calculators can make it easier to calculate percentages, especially when working with large numbers.

Q: What are some common mistakes to avoid when calculating percentages?

A: Some common mistakes to avoid when calculating percentages include:

  • Rounding errors: Make sure to round your answer to the correct decimal place.
  • Unit errors: Make sure that both quantities are in the same unit before calculating the percentage.
  • Sign errors: Make sure to use the correct sign (positive or negative) when calculating a percentage increase or decrease.

Q: How can I practice calculating percentages?

A: You can practice calculating percentages by working through examples and exercises. You can also use online resources, such as calculators and worksheets, to help you practice.

Q: What are some real-world applications of calculating percentages?

A: Calculating percentages has numerous real-world applications, including:

  • Finance: Calculating interest rates, investment returns, and credit card balances.
  • Science: Calculating concentrations, percentages, and ratios in chemical reactions.
  • Engineering: Calculating efficiency rates, power consumption, and energy usage.

By practicing and mastering the concept of expressing quantities as percentages, you'll be able to apply this skill in various real-world scenarios and make informed decisions in your personal and professional life.