Problem 14 - Elementary Algebra

Question

For the following problems, convert each decimal to a percent. $$ 0.42 $$

Step-by-Step Solution

Answer

Answer: 42%

Step 1: Identify the decimal number

In this exercise, the decimal number given is 0.42.

Step 2: Convert the decimal number to a percentage

To convert the decimal number to a percentage, multiply it by 100: $$ 0.42 \times 100 = 42 $$

Step 3: Add the percent sign

Now that we have found the equivalent percentage (42), we can add the percent sign to our answer: $$ 42\% $$ The decimal number 0.42 is equal to 42%.

Key Concepts

Understanding Decimal Numbers

When we talk about decimal numbers, we refer to numbers that have a whole part and a fractional part, separated by a decimal point. The number to the right of the decimal point represents a fraction of a whole. For example, in the numeric value 0.42, the '4' is in the tenths place, implying 4 tenths, while the '2' stands for two hundredths, making it a precise way to express values between whole numbers.

It's essential to recognize that the place value system plays a pivotal role in understanding decimals. Every move to the right of the decimal point indicates a smaller unit - tenths, hundredths, thousandths, and so on. This concept is fundamental when converting decimals to other forms, such as percents, because it allows us to depict the same value in different ways depending on what's needed for calculations or to represent data.

Percentage Conversion Explained

Percentage conversion is a method used to represent decimal numbers as a part of 100. This is often used to compare numbers, understand proportions better, or simply adhere to conventions in fields like statistics or finance. To convert a decimal to a percentage, you essentially move the decimal point two places to the right. This action is akin to multiplying by 100, which scales the number up to how many 'parts out of 100' it represents.

This process is particularly user-friendly because it eliminates the decimal point, allowing individuals to interpret quantities in terms of percents - a concept that's generally ingrained in our understanding from a young age. Whether it's calculating sales tax or figuring out what portion of a class passed a test, converting decimals to percentages provides a universally recognized way to communicate quantities.

Multiplying Decimals by 100

Multiplying by 100 is the core mathematical operation when converting a decimal to a percent. The reason for this is that 'percent' literally means 'per hundred.' So, when you multiply a decimal by 100, you're finding out how many parts out of 100 it represents. Let's take the decimal 0.42 as our example again. When you multiply this decimal by 100, you're shifting the decimal point two places to the right, giving you 42.

Multiplying by 100 is straightforward, but there's a practical reason for this operation. By understanding that you're shifting the decimal point to obtain a percentage, you establish a reliable and quick method to convert decimals during calculations. This not only aids in mathematical prowess but also improves your conceptual understanding of the relationships between fractions, decimals, and percentages.