Problem 81 - Algebra A Combined Function

Question

Write each decimal as a percent. $$ 1.92 $$

Step-by-Step Solution

Answer

1.92 as a percent is 192%.

Step 1: Understanding Decimal to Percent Conversion

To convert a decimal number to a percent, you multiply the decimal by 100. This is because percentage is essentially a fraction with a denominator of 100.

Step 2: Multiply by 100

Take the decimal number 1.92 and multiply it by 100. \[ 1.92 \times 100 = 192 \]

Step 3: Add the Percent Symbol

After the multiplication, add the percent symbol to the result to express it as a percentage. Thus, 1.92 as a percent is 192%.

Key Concepts

Multiplying Decimals

Understanding how to multiply decimals is crucial in many mathematical conversions, like turning a decimal into a percent. To multiply decimals, we use the same basic rules as regular multiplication. The difference is the placement of the decimal point in the final answer. For example, if you multiply decimal numbers like 1.92 by 100, you perform the basic multiplication first: 192.
Next, you keep track of the decimal places. Since 1.92 has two numbers after the decimal point, you shift the decimal two places to the right in your product (192.0). Multiplying by 100 effectively moves the decimal two places, giving you a whole number.
When multiplying, it's always a good idea to remember:

• Ignore the decimals initially – multiply as if they’re whole numbers.
• Count the total decimal places from the numbers you’re multiplying.
• Adjust the decimal in the result based on this count.

Through careful placement, you ensure your calculations are accurate and the decimal conversion correct.

Understanding Percentages

Percentages are a way to express numbers as parts of 100. Saying "92%" means 92 out of every 100 parts. This concept simplifies comparing quantities and determining proportions. Whenever you want to write a decimal as a percentage, you essentially tell how many parts out of 100 correspond to the original number.
In our exercise, when 1.92 is converted to a percentage, it becomes 192%. This indicates that 1.92 is equivalent to 192 out of 100, which is slightly intuitive. This conversion helps easily read or compare scenarios, like comparing results among different categories or changes. Some real-world contexts where understanding percentages is key include sales discounts, statistics, and interest rates.
With percentages:

• They often offer a clearer picture in finance, statistics, and everyday comparisons.
• They allow for easy computation of increases and decreases through percentage changes.
• The conversion process solidifies one's understanding of part-whole relationships.

Mathematical Notation

Mathematical notation is a universal language used to describe mathematical concepts simply and clearly. It includes numbers, symbols, and expressions that depict math operations, relationships, and values. In our conversion exercise, mathematical notation was used to denote multiplication and percentage.
The notation \[ 1.92 \times 100 = 192 \]clearly expresses that the decimal 1.92 is multiplied by 100, which is essential in converting to a percentage. Notation standardizes processes and makes them easy to communicate and understand.
The final step required adding a percent symbol, notated as %.
Using mathematical notation:

• Provides a concise way to express long operations or processes.
• Allows for international understanding and consistency in math-related activities.
• Helps in systematically solving problems and either verifying or communicating solutions.

With a solid grasp of notation, you can easily decipher and write out mathematical procedures effectively.