Problem 79 - Algebra A Combined Function

Question

Write each decimal as a percent. $$ 0.5 $$

Step-by-Step Solution

Answer

0.5 as a percent is 50%.

Step 1: Understand the Conversion

To convert a decimal to a percent, you need to multiply the decimal by 100. This is because 'percent' means 'per hundred', so multiplying by 100 will shift the decimal point two places to the right, effectively showing how many parts out of 100 the decimal represents.

Step 2: Perform the Calculation

Take the decimal value, 0.5, and multiply it by 100:\[ 0.5 \times 100 = 50 \]This calculation converts the decimal to a percent.

Step 3: Interpret the Result

The result of the calculation, 50, means that 0.5 is equivalent to 50% when expressed as a percentage.

Key Concepts

Understanding Decimal Multiplication

When multiplying decimals, the process is similar to whole number multiplication. However, there's an important step added at the end to adjust for the decimal places. To multiply decimals:

• Ignore the decimal points initially and multiply the numbers as if they were whole numbers.
• Count the total number of decimal places in both of the original numbers.
• After multiplication, place the decimal point in the result; it should have as many decimal places as the total from both numbers combined.

For example, when you multiply 0.5 by 100, treat it first as 5 times 100. The result is 500. Since there is one decimal place in 0.5, shift the decimal one place back in 500, resulting in 50.

Simplifying Percent Calculation

Calculating a percent involves understanding what percent means: 'per 100'. Thus, converting from a decimal to a percent is making a comparison to 100. This means shifting the decimal two places to the right.

• Taking a decimal, say 0.5, to convert it into a percent, multiply by 100.
• The multiplication (0.5 × 100) results in 50, showing 50 parts out of 100 or 50%.
• This process effectively visualizes what fraction of a hundred you are dealing with.

This conversion approach highlights how decimals relate to parts of a whole in percentage terms.

Grasping Mathematical Conversion

Mathematical conversion is used to change numbers from one format to another. This can include converting decimals to fractions, fractions to percentages, or other transformations.

• When converting a decimal such as 0.5 to a percent, interpret the number in a new context: per 100 units.
• Multiplying by 100 accomplishes this conversion swiftly, giving a clear percentage representation.
• Understanding conversion is crucial in many mathematical problems, where different forms offer various insights or simplifications.

These conversions are foundational in math, enabling clear communication of values among different people and disciplines.