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Converting a percentage into a decimal is an essential skill in mathematics. This is because percentages are often expressed out of 100, but decimals are a more universal format that can be easily added, subtracted, or multiplied. To convert a percentage into a decimal, you divide the percentage by 100. This process shifts the decimal point two places to the left. For example, if you have 7.5%, you transform it by calculating \( \frac{7.5}{100} \), which equals 0.075.This conversion works smoothly because percentages represent parts per hundred. As a result, dividing by 100 makes them "per one" or decimals, which are easier to work with in most equations.

Multiplying decimals may seem tricky at first, but it follows a straightforward process once you know the steps. Let's dive into how you can comfortably multiply decimals like a pro. Once you convert a percentage to a decimal, you can multiply it by another number. In our exercise, we converted 7.5% to 0.075, and now we want to find 7.5% of 340. Multiply 0.075 by 340 to get our result. Here's a simple way to multiply decimals:

• Ignore the decimal points and multiply the numbers as if they are whole numbers.
• Count the total number of decimal places in both numbers involved in the multiplication.
• Place the decimal point in the product, ensuring it has the same number of decimal places from the previous count.

Example: Multiplying 0.075 (three decimal places) by 340 (zero decimal places) involves multiplying 75 by 3400 first and then placing the decimal point three numbers from the end, resulting in 25.5.

Equation solving appears frequently across mathematics and real-life situations, helping us find unknown numbers or verify if numbers satisfy conditions. An equation states two expressions are equal and includes unknown values, often called variables.Let's consider the exercise: Find 7.5% of 340. We already know the decimal equivalent from earlier.Formulate the equation using a variable \( x \), where \( x \) represents the unknown:\[ 0.075 \times 340 = x \]Calculate by performing the multiplication. In this case, \( x = 25.5 \), so 7.5% of 340 equals 25.5. This process of setting up an equation, converting the percentage, and simplifying confirms our solution and helps understand solving equations.