Problem 49 - Algebra 2

Question

Find each percent. 68% of 200

Step-by-Step Solution

Answer

68% of 200 is 136.

Step 1: Understand the Problem

We need to find what 68% of 200 is. This means we need to calculate 68% of the number 200.

Step 2: Convert Percentage to Decimal

Percentages are parts per hundred. To convert 68% to a decimal, divide 68 by 100. So, 68% becomes 0.68 as a decimal.

Step 3: Perform Multiplication

Multiply the decimal form of the percentage by the total number. This means we calculate 0.68 multiplied by 200. This gives us 0.68 * 200 = 136.

Step 4: State the Result

The result of the multiplication is 136. This means 68% of 200 is 136.

Key Concepts

Percentage Calculation

When you hear the term "percentage," you might think of it as a way to express how much of something is contained within a whole. A percentage is essentially a fraction of 100. For example, if you have 68%, it means 68 per 100.
This is useful for many real-life calculations like figuring out sales tax, discounts, or determining grades. To find a percentage of a number, follow these general steps:

• First, convert the percentage into a decimal.
• Then, multiply the decimal by the number you want to find the percentage of.

For instance, to find 68% of 200, you multiply 0.68 by 200. This will give you the exact portion out of the number related to the percentage, so 68% of 200 equals 136.

Decimal Conversion

Decimal conversion is a crucial step in calculations involving percentages. It simplifies the multiplication process by converting percentages into a form that is easier to handle mathematically. Converting a percentage to a decimal is straightforward:

• Take the percentage value and divide it by 100.
• For example, to convert 68% into a decimal, divide 68 by 100, giving you 0.68.

With decimals, you can perform calculations like multiplication more easily, without getting tangled in fractions or percentages themselves. This conversion serves as the bridge that transforms a percentage into a usable form in calculations, making complex processes more approachable.

Multiplication in Mathematics

Multiplication in mathematics is one of the four basic operations, alongside addition, subtraction, and division. It may seem simple, but it plays a pivotal role in solving real-world problems involving percentages and more. To multiply, you combine groups of numbers equally. When dealing with decimal numbers:

• Align decimal points and proceed as with whole numbers, then adjust the decimal in the result.
• For instance, when multiplying 0.68 by 200, you obtain 136.

In percentage calculations, such multiplication determines how much of the whole is represented by the given percentage. Mastering this operation allows you to handle a variety of mathematical situations with confidence.