Problem 61 - Algebra 1

Question

Find the number. $$ 76 \% \text { of } 540 $$

Step-by-Step Solution

Answer

The result of 76% of 540 is 410.4

Step 1: Convert percentage to a decimal

To convert a percentage to a decimal, divide the percentage by 100. So, 76% should be divided by 100 to get 0.76.

Step 2: Multiply the decimal by the given number

Multiply the decimal obtained in the first step by the given number (540). So, 0.76 times 540 equals 410.4

Key Concepts

Converting Percentages to Decimals

When dealing with percentages, it's often necessary to convert them into decimals to perform various mathematical operations. So, how do you convert a percentage to a decimal? The key is to divide the percentage by 100. This is because 'percent' means 'per hundred', so 76% is literally 76 per 100 or \( \frac{76}{100} \).

Thus, to convert 76% to a decimal, you simply divide 76 by 100, which gives you 0.76. This simple conversion method allows us to seamlessly shift from percentages, which are useful for expressing ratios, to decimals, which are better suited for further calculations.

Multiplying Decimals

Once you've converted your percentage into a decimal, you may need to use it in further calculations, such as finding a certain percentage of a number. Multiplication involving decimals follows the same principles as with whole numbers.

However, it's important to line up the numbers by their rightmost digits (not by the decimal point) and then perform the multiplication as usual. Afterward, the total number of digits after the decimal in the factors is counted, and the decimal point is placed in the product accordingly. For instance, multiplying 0.76 by 540, you align the numbers and multiply as if they were whole numbers. You then count the decimal places in the decimal number (two places in 0.76), ensuring the product, 410.4, has the same number of decimal places.

Mathematical Operations with Percentages

Performing mathematical operations with percentages is a fundamental skill in various fields of study and everyday situations. Once percentages have been converted to decimals, as previously mentioned, they can be used in multiple operations such as addition, subtraction, multiplication, and division.

For example, finding 76% of 540 requires a multiplication of the decimal form of the percentage (0.76) by the whole number (540). This conceptual application allows for determining parts per hundred in tangible terms – in this case, what 76 out of every 100 parts of the number 540 would equate to, providing a concrete answer of 410.4. Understanding these operations with percentages equips one with the ability to tackle problems set in financial contexts, data analysis, and even everyday grocery shopping discounts.