Problem 16 - Prealgebra

Question

Change each percent to a decimal. $$5.8 \%$$

Step-by-Step Solution

Answer

The decimal form of 5.8% is 0.058.

Step 1: Understanding Percent to Decimal Conversion

A percentage is a way of expressing a number as a fraction of 100. To convert a percent to a decimal, you need to move the decimal point two places to the left.

Step 2: Shift the Decimal Point

Take the percentage value, 5.8%, and move the decimal point two places to the left. This operation transforms 5.8 into 0.058 as a decimal.

Step 3: Remove the Percent Sign

After shifting the decimal point, write down the number that remains without the percent sign: 0.058.

Key Concepts

Decimal Point Movement

When converting percentages to decimals, the movement of the decimal point is key. This operation involves shifting the decimal point in the percentage figure two places to the left. Why two places? Because a percent is essentially a number divided by 100.
Think of 5.8% as 5.8 divided by 100. By moving the decimal point two spots to the left, you've effectively performed that division. So, 5.8% becomes 0.058 in decimal form.

• Step 1: Locate the decimal point in the percentage.
• Step 2: Move the decimal point two places to the left.
• Step 3: What you see is the decimal equivalent.

This simple movement of the decimal point allows us to seamlessly switch between formats, retaining the same value in a different structure.

Educational Math Concepts

Understanding decimal and percent conversions is tied to grasping some fundamental educational math concepts. These concepts serve as the building blocks for a variety of calculations you'll encounter in math.
A percent is a way of expressing a number out of 100. Knowing how to convert it helps in diverse situations, including everyday contexts like calculating discounts or determining interest rates.

• Percent to decimal is a form of unit conversion, much like inches to centimeters.
• This understanding aids in interpreting results and ensuring accuracy across different mathematical problems.
• It also provides practice in visualizing and manipulating numbers in multiple formats.

As you practice, these concepts become instinctual, making you more adept at handling percentages and decimals.

Basic Math Operations

The process of converting a percentage to a decimal underscores the simplicity and utility of basic math operations, particularly division and multiplication by powers of ten.
The division operation is implicit when we move the decimal point to convert a percent to a decimal. By doing this, you are engaging in an operation mathematically equivalent to dividing by 100. Multiplication comes into play because once you have the decimal form, multiplying by 100 gives you back the percent.

• Converting 5.8% to a decimal is the same as calculating 5.8 divided by 100.
• Remember: moving the decimal point and dividing or multiplying by 100 yield the same results, just different methods of arriving.
• These operations give insights into deeper mathematical processes and enable more complex calculations down the line.

Mastering these basic operations is not just about solving textbook problems, but equipping oneself with skills for real-world application.