Problem 15 - Prealgebra

Question

Change each percent to a decimal. $$3.4 \%$$

Step-by-Step Solution

Answer

3.4% as a decimal is 0.034.

Step 1: Understanding Percent

A percent is a way of expressing a number as a fraction of 100. Therefore, 3.4% means 3.4 out of 100.

Step 2: Conversion Formula

To change a percent into a decimal, divide the percent value by 100. This is because 'percent' literally means 'per hundred'.

Step 3: Applying the Conversion

Divide 3.4 by 100. In mathematical terms, this is represented as: \( 3.4 \div 100 \).

Step 4: Performing the Calculation

When you divide 3.4 by 100, you move the decimal point two places to the left, resulting in 0.034.

Key Concepts

Understanding Percents

Understanding percents is essential in the world of mathematics and daily life. A percent is a way of expressing a number as a fraction of 100. For example, when you say 3.4%, you are actually referring to 3.4 out of 100. The term "percent" comes from the Latin phrase "per centum," which means "by the hundred."

Here's why percentages are useful:

• They provide a concise way to express proportions and comparisons.
• They help to standardize any kind of data, which can then be easily compared.
• Percentages are widely used in financial contexts, like calculating interest rates, discounts, or tax rates.

In educational settings, understanding percentages is crucial for advancing in math, as they form a foundational part of many mathematical operations and applications.

Decimal Conversion

Converting percentages to decimals is a simple yet fundamental mathematical skill. When you convert a percentage into a decimal, you are scaling it down from a fraction of 100 to a fraction of 1, which is more useful in precise calculations. This is done by dividing the percentage value by 100.

The steps to convert from a percent to a decimal include:

• Identify the percentage value, for instance, 3.4%.
• Recognize that the term 'percent' means 'out of 100'.
• Divide the percentage by 100, which moves the decimal point two places to the left, effectively bringing it into the realm of decimals.

After conversion, 3.4% becomes 0.034 in decimal form. This practice of conversion is vital in various situations where precision is required, especially in mathematical equations and financial calculations.

Performing Mathematical Calculations

Carrying out mathematical calculations involving percentages and decimals is a practical skill. When you encounter a percentage, transforming it into a decimal simplifies the process of performing most mathematical operations like multiplication, division, or algebraic expressions.

To perform the calculation:

• Start with your percentage value, such as 3.4%.
• Convert this percentage into a decimal by dividing by 100, resulting in 0.034.
• Perform calculations like multiplication with ease, because working with decimals in equations is generally more straightforward than using percentages.

If you want to multiply a value by 3.4%, first convert it to 0.034, and then multiply. This ensures accuracy and consistency in your calculations. Mastering this skill allows for efficient handling of a wide range of mathematical and real-world scenarios.