Problem 52 - Prealgebra

Question

Write as a percent. $$0.05$$

Step-by-Step Solution

Answer

0.05 as a percentage is 5%.

Step 1: Understanding the Concept

The problem requires converting the decimal number 0.05 into a percentage. Understanding that the percentage is a way of expressing a number as a fraction of 100 is crucial for solving this exercise.

Step 2: Conversion Formula

Any decimal can be converted to a percentage by multiplying by 100. This is because 'percent' literally means 'per hundred.' So, we will use the formula: \[ \text{Percentage} = \text{Decimal} \times 100 \]

Step 3: Applying the Formula

Substitute the decimal 0.05 into the formula: \[ \text{Percentage} = 0.05 \times 100 \]Carry out the multiplication to convert the decimal to a percentage.

Step 4: Calculating the Percentage

Perform the multiplication:\[ 0.05 \times 100 = 5 \]Hence, 0.05 as a percentage is 5%.

Step 5: Final Answer

The conversion is complete, resulting in 0.05 expressed as a percentage being 5%.

Key Concepts

Decimal Conversion

Decimal conversion is the process of turning decimals into other forms, such as percentages. This concept helps in understanding and comparing quantities expressed in different ways. To convert a decimal to a percentage, you multiply the decimal by 100, because 'percent' means 'per hundred'. This process allows you to express the decimal as a part of 100, making it a percentage.
For example, if you have the decimal 0.05, converting it to a percentage involves multiplying it by 100, which gives you 5%. So, 0.05 as a percentage is 5%. Understanding decimal conversion is essential in various mathematical and everyday applications. It makes working with numbers more intuitive, especially in contexts involving financial calculations, probabilities, and statistics.

Multiplication

Multiplication is one of the basic operations in arithmetic, representing the process of repeated addition. It is vital in decimal conversions, where it is used to scale a decimal so that it can be expressed as a percentage. When we multiply a decimal by 100, we are essentially shifting the decimal point two places to the right.

• The formula to convert a decimal to a percentage is: \[ \text{Percentage} = \text{Decimal} \times 100 \]
• This operation relies on the basic principle that each multiplication by 10 moves the decimal one place to the right.

In our exercise, multiplying 0.05 by 100 moves the decimal two places, transforming it from a fractional form to a whole number, 5. As you practice these techniques, you'll notice multiplication is a key skill that opens doors to solving many math problems, including decimal and percentage conversions.

Basic Arithmetic

Basic arithmetic includes four core operations: addition, subtraction, multiplication, and division. These are foundational skills in mathematics, each operation allowing us to manipulate numbers in different ways. Understanding basic arithmetic helps in performing tasks such as converting numbers, calculating percentages, and solving everyday math problems.
In terms of decimal percentage conversions, basic arithmetic simplifies the process. For example, when converting 0.05 to a percentage, you leverage multiplication, which is one of the arithmetic operations.

• By knowing arithmetic operations, particularly multiplication, you can easily convert decimals to percentages and vice versa.
• Arithmetic skills also help recognize patterns and perform calculations mentally or with minimal tools.

Learning basic arithmetic sets the groundwork for more advanced mathematical concepts, enabling a deeper understanding of different numerical forms and operations.