Problem 27 - Elementary Algebra

Question

For the following problems, convert each percent to a decimal. $$ 9.0145 \% $$

Step-by-Step Solution

Answer

Question: Convert the percentage 9.0145% to a decimal form. Answer: 0.090145

Step 1: Write the given percentage as a fraction

We are given 9.0145%. To convert it to a fraction, we write it as $$\frac{9.0145}{100}$$.

Step 2: Divide by 100 to convert to decimal

Now, we simply need to divide the numerator 9.0145 by the denominator 100. Using a calculator, we get: $$\frac{9.0145}{100} = 0.090145$$

Step 3: Write the final answer

The percentage 9.0145% has been successfully converted to the decimal form 0.090145.

Key Concepts

Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100. The symbol for percentage is % and it means "per hundred." This is a very useful concept because it allows us to easily compare ratios and proportions. It's commonly used in areas like finance, statistics, and everyday scenarios such as discounts in shopping.
For instance, if you have 9.0145%, it means 9.0145 per 100 units. Think of percentages as an easy way to relate quantities to a standard base of 100.

• Percentages are often used to describe parts of a whole.
• They help in understanding and comparing different quantities in a standard way.
• In our exercise, converting 9.0145% helps in understanding the proportion of the quantity in relation to 100.

Decimal Conversion Made Simple

Converting percentages to decimals is straightforward. You can think of decimals as another way to represent parts of a whole. When you convert a percentage to a decimal, you're simply adjusting the number to eliminate the percentage sign (%).
To do this, divide the percentage number by 100. It's like scaling back the value to fit into a single whole number rather than a part of 100.
For example:

• Step 1: Write the percentage as a fraction. For 9.0145%, it becomes \( \frac{9.0145}{100} \).
• Step 2: Convert the fraction to a decimal by dividing the number by 100, which gives 0.090145.

This systematic approach ensures accuracy and is easy to apply across different percentage calculations.

The Mathematical Calculation Process

Mathematical calculations often hinge on understanding how numbers relate to each other. Conversion from percentage to decimal is a two-step process involving simple division.
To convert 9.0145% into a decimal:

• Express the percentage out of 100 as a fraction: \( \frac{9.0145}{100} \).
• Now perform the division: 9.0145 divided by 100 equals 0.090145.

Tools such as calculators can make this process quicker, especially when dealing with long decimal numbers. It's always good to double-check your calculations to ensure accuracy.
This method is reliable, giving a precise decimal representation. Doing these calculations can become second nature with practice, allowing you to apply the concept to various mathematical and real-world scenarios effectively.