Problem 27 - Algebra A Combined Function

Question

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. See Examples 1 through 6. Find \(23 \%\) of 20.

Step-by-Step Solution

Answer

23% of 20 is 4.6.

Step 1: Convert the Percentage to a Decimal

To find 23% of 20, the first step is to convert the percentage to a decimal. Percent means per hundred, so to convert a percentage to a decimal, you divide by 100. Thus, \(23\% = \frac{23}{100} = 0.23\).

Step 2: Multiply the Decimal by the Whole Number

Now that we have the percentage as a decimal (0.23), we multiply it by the whole number 20 to find 23% of 20. \[0.23 \times 20 = 4.6\]

Step 3: Present the Answer

The calculated result should be presented with the correct level of precision as requested by the problem. For this problem, ensure that the answer is rounded to one decimal place as needed.

Key Concepts

Decimal Conversion

Decimal conversion is a crucial skill when working with percentages. Let's break it down. A percentage represents a number out of one hundred, which means it's essentially a fraction atop the denominator of 100. To convert from a percentage to a decimal, you simply divide by 100. This transforms the percent into a more manageable decimal form that we can work with in calculations. For instance, to convert 23% to a decimal, you perform the calculation: \[23\, \text{percent} = \frac{23}{100} = 0.23\]With this conversion, you can easily proceed to further mathematical operations such as multiplication, which can be tricky with percentages.

Multiplication of Decimals

Once you've converted a percentage to a decimal, the next step is multiplying it by another number to find the desired portion. Multiplying decimals might seem daunting at first, but it's quite straightforward. Here's a step-by-step guide to make it easier:

• Ignore the decimal points and multiply the numbers as if they were whole numbers.
• Count the total number of decimal places in the two factors. This tells you how many decimal places the product should have.
• Place the decimal point in the result accordingly.

For example, when multiplying 0.23 by 20 to find 23% of 20, treat it like multiplying 23 by 20. Then, apply the decimal as needed:\[0.23 \times 20 = 4.6\]This step reveals the percentage of the whole, maintaining the decimal's integrity throughout the process.

Rounding Numbers

Rounding numbers is vital for presenting clear and simplified results, especially in contexts like currency, where excessive decimal places can confuse. Follow these straightforward steps to round numbers:

• Identify the place value you need to round off to. For many scenarios, this might be to the nearest hundredth for money or nearest tenth for other figures.
• Look at the digit immediately next to your rounding place. If it's 5 or higher, round up. If it's lower, keep the digit unchanged.

In our example, the answer 4.6 is already rounded to one decimal place. This ensures clarity and meets the problem's requirements without additional rounding needed.

Mathematical Precision

Precision refers to the level of detail in a numerical representation. In mathematics, especially when dealing with decimals and percentages, understanding precision is essential to ensure accurate calculations and results.

• Precision is about ensuring that your calculations reflect the true value as closely as required by the context. Different scenarios may require different levels of precision.
• A precise answer doesn't always mean more decimal places. Sometimes, it means having the right number of decimals relevant to the problem.
• In problems specifying a certain precision level, double-check that your final number conforms to these demands.

By rounding to one decimal place for a calculation like 4.6, you're aligning with the exercise's specifications, ensuring both accuracy and conciseness in your result.