Question

Find each result using any method you like. \(45 \%\) of 234

Short answer

105.3

Step-by-step solution

- Understand what percent means

A percent represents a part of a whole and is expressed as a fraction out of 100. For example, 45% means 45 parts out of 100.

- Convert the percentage to a decimal

To convert 45% to a decimal, divide by 100: \[ 45\text{%} = \frac{45}{100} = 0.45 \]

- Multiply the decimal by the whole number

Multiply the decimal form by the whole number to find 45% of 234: \[ 0.45 \times 234 \]

- Perform the multiplication

Calculate the product: \[ 0.45 \times 234 = 105.3 \]

Key concepts

percent-to-decimal-conversion

A percent represents parts per hundred. When converting a percentage to a decimal, you effectively move the decimal point two places to the left. This is because a percentage is already out of 100.

For example, to convert 45% to a decimal:

• Imagine 45% as \( \frac{45}{100} \).
• When you divide 45 by 100, you get 0.45.

\[ 45\% = \frac{45}{100} = 0.45 \]
Converting percentages to decimals simplifies further calculations.

multiplication-of-decimals

Once you have a decimal, the next step is to perform multiplication. Multiplying decimals is similar to multiplying whole numbers, but with a focus on where the decimal point should be in the result.

Here's an example using our earlier decimal: 0.45. To find 45% of 234, multiply 0.45 by 234:

• Ignore the decimal points at first: 45 * 234.
• Multiply as usual: 45 * 234 = 10530.
• Count the total decimal places from the numbers being multiplied (in this case, two from 0.45 and none from 234).
• Place the decimal point in the answer, two places from the right: 105.30 or just 105.3.

Thus, 0.45 multiplied by 234 gives us 105.3.

finding-a-percentage-of-a-number

Finding a percentage of a number is a common task in many areas such as finance, shopping, and statistics. It involves converting the percentage to a decimal and then multiplying by the number in question.

To find 45% of 234, follow these steps:

• Convert 45% to a decimal, which is 0.45.
• Multiply 0.45 by 234.
• Calculate the product: \[ 0.45 \times 234 = 105.3. \]

The final answer is 105.3, meaning that 45% of 234 is 105.3.
Breaking down the problem into smaller manageable steps helps in understanding the process better and achieving accurate results.