Problem 17 - Prealgebra

Question

Change each percent to a decimal. $$6.34 \%$$

Step-by-Step Solution

Answer

6.34% as a decimal is 0.0634.

Step 1: Understanding Percent and Decimal

To convert a percentage to a decimal, remember that a percent (%), means 'per hundred.' So, 6.34% is equivalent to 6.34 per 100.

Step 2: Remove the Percent Symbol

The first step in converting a percentage to a decimal is to remove the percent symbol (%) from the number. For 6.34%, we start by considering the number 6.34.

Step 3: Divide by 100

Since percent represents a fraction out of 100, divide the number by 100 to convert it into a decimal. So, you divide 6.34 by 100: \[\frac{6.34}{100} = 0.0634\]

Step 4: Explanation of Movement of Decimal

Dividing by 100 has the effect of moving the decimal point two places to the left. In this case, moving the decimal point two places to the left converts 6.34 to 0.0634.

Key Concepts

Understanding Percentages

Percentages are all around us and understanding them is crucial in everyday life. A percentage is essentially a way to express a number as a part of a whole, specifically out of 100. When you see a number like 50%, it simply means 50 out of 100, which visualizes as half of something. Looking at percentages helps you easily compare quantities, understand discount rates, or even determine growth.

Whenever you encounter a percentage and need to do calculations, start by remembering that the '%' sign is a reminder of dividing by 100. If you grasp this basic idea, it becomes so much easier to handle conversions and arithmetic involving percentages. For instance, 6.34% can be understood as 6.34 per every 100 units. It's a simple yet powerful way of representing parts of a whole in various contexts.

Decimal Conversion

Converting percentages into decimals is a practical skill useful in various math and real-life situations. Decimals are just another way of expressing fractions and percentages. Converting a percentage to a decimal allows you to perform computations more easily.

To convert a percentage like 6.34% to a decimal, follow a straightforward process. First, remove the percent sign, turning it into a plain number: 6.34. This step is essential to clearly isolate the numerical value. Next, to truly turn the percentage into decimal format, divide by 100. This division changes the number from a part of 100 (a percentage) to part of 1 (a decimal). For example:

• Divide 6.34 by 100: i.e. \({\frac{6.34}{100} = 0.0634}\)
• Notice how the decimal point shifts two places to the left, illustrating the division by 100.

Practicing this conversion helps you become adept in switching between formats, which is useful in any mathematical computations involving percentages.

Arithmetic Operations

Understanding how to handle arithmetic operations with decimals and percentages is key to solving real-world mathematical problems. Once you convert percentages to decimals, performing arithmetic operations becomes simpler and more straightforward.

Arithmetic operations refer to basic mathematical processes like addition, subtraction, multiplication, and division. When you have percentage-related problems, converting to decimals can make these operations easier to carry out.

• For addition and subtraction, ensure that your decimals are aligned by place value.
• For multiplication, multiply as with whole numbers, and then count the total number of decimal places in both factors to correctly place the decimal point in the product.
• Division involves understanding how to handle decimals where you might need to multiply divisor and dividend to eliminate the decimal to simplify operations.

Imagine calculating a sale discount: start by converting the percentage off to a decimal, then multiply by the price. This approach helps establish a solid foundation for effectively managing arithmetic tasks involving percentages and decimals.