Problem 22 - Technical Mathematics with Calculus

Question

Find: $$50.8 \% \text { of } \$ 245$$

Step-by-Step Solution

Answer

\(50.8\% \text{ of } \)245 \text{ is } $124.46.

Step 1: Convert Percentage to Decimal

To find a percentage of a number, first convert the percentage to a decimal by dividing by 100. For 50.8%, divide 50.8 by 100.

Step 2: Multiply Decimal by the Amount

Multiply the decimal obtained in step 1 by the total amount, in this case, \(245, to find 50.8% of \)245.

Key Concepts

Convert Percentage to Decimal

Understanding how to change a percentage into a decimal is an essential skill in mathematics that allows for easier handling of these numbers in various calculations. To convert a percentage to a decimal, simply divide the percentage by 100. This shifts the decimal point two places to the left.

For example, if we have a percentage like 50.8%, we divide 50.8 by 100, leading to 0.508. Why do we do this? It's because 'percent' means 'per hundred', so we're effectively extracting the proportion of the value per hundred units translated into a more manageable form used in other calculations.

Multiplying Decimals

When it comes to multiplying decimals, the position of the decimal point is crucial. To effectively multiply a decimal by another number, simply perform the multiplication process as if you were dealing with whole numbers, and then place the decimal point in the product.

The important step is determining the right position of the decimal in the answer. For instance, if we multiply 0.508 (converted from 50.8%) by a whole number like 245, multiply as usual: 508 x 245. Then, count the number of decimal places in the original decimal – here it's three places. In the final product, count three places from the right to place the decimal, which will give you the correct result in decimal form.

Mathematical Operations

Performing mathematical operations such as addition, subtraction, multiplication, and division with decimals is akin to working with whole numbers, but it requires careful attention to the placement of the decimal point.

Each operation follows specific rules regarding how to handle decimals. When adding or subtracting, decimals should be lined up vertically to ensure accurate results. During multiplication, as discussed earlier, count the total number of decimal places in all the numerals to place the decimal point correctly in the answer. While dividing, you may sometimes need to adjust the divisor to a whole number by moving the decimal point, a movement that also applies to the dividend. Always verify the results by estimating to check if the answer is reasonable within the context of the original problem.