Question

Find each result using any method you like. \(72 \%\) of 3.7

Short answer

2.664

Step-by-step solution

- Convert the Percentage to a Decimal

To find 72% of 3.7, first convert the percentage to a decimal. Divide 72 by 100: \[ 72 \times \frac{1}{100} = 0.72 \]

- Multiply the Decimal by the Number

Next, multiply the decimal (0.72) by 3.7: \[ 0.72 \times 3.7 \]

- Perform the Multiplication

Calculate the result of the multiplication: \[ 0.72 \times 3.7 = 2.664 \]

- Round if Necessary

If needed, round the answer to a desired number of decimal places. For this problem, you can leave it as 2.664 because it's already a reasonable precision.

Key concepts

Converting Percentages to Decimals

When working with percentages, it's often easiest to convert them into decimal form. This helps in performing mathematical operations like multiplication. To do this conversion, you can use a simple rule: divide the percentage by 100. For example, take 72%. Divide it by 100:

• 72 ÷ 100 = 0.72

Now, 72% is represented as 0.72 in decimal form. This step is essential because it makes subsequent calculations more straightforward and less error-prone. Always remember: dividing by 100 moves the decimal point two places to the left.

Multiplication of Decimals

Once you've converted percentages to decimals, you can easily multiply. Multiplying decimals may seem tricky at first, but it's quite similar to multiplying whole numbers. Here's how to multiply 0.72 by 3.7:

• First, ignore the decimal points and multiply the numbers as if they were whole numbers: 72 × 37 = 2664.
• Next, count the total number of decimal places in both of the original numbers. 0.72 has two decimal places, and 3.7 has one decimal place, for a total of three decimal places.
• Finally, place the decimal point in your product (2664) so that it has three decimal places: 2.664.

So, 0.72 × 3.7 gives you 2.664. Be mindful of how many decimal places your final answer should have by counting the decimal places in the numbers you are multiplying.

Rounding Numbers

Sometimes, you'll need to round your final answer to a specific number of decimal places. Rounding makes numbers easier to work with and understand. Here's how to round a number correctly:

• Identify the place to which you want to round. For example, let's say we want to round 2.664 to two decimal places.
• Look at the digit immediately to the right of this place (hundredths place in our example): the number is 4.
• If this digit is 5 or higher, round up. If it's 4 or lower, keep the rounding place digit the same.

So in our example: 2.664 rounded to two decimal places is 2.66. Rounding is important for approximations and making results easier to report.