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Understanding the relationship between percentages and decimals is essential in everyday math. To convert a percentage into a decimal, you start with the basic knowledge that 1% is equivalent to the decimal 0.01. This is because the word 'percent' means 'per hundred', so 1% is 1 out of 100, and as a decimal, that's 0.01.

When dealing with percentages that are not whole numbers, such as \( \frac{1}{2} \% \), you still apply the same principle. Imagine sliding the decimal point two places to the left as you convert from a percentage to a decimal. For \( \frac{1}{2} \% \), which is half of 1%, you would first convert 1% to 0.01 and then simply divide by 2 to get 0.005.

The process can be visualized in a more general form as well: if you have a percentage like A%, its decimal equivalent is \( \frac{A}{100} \). This approach helps simplify the conversion process and ensures accuracy.

Once you've converted a percentage to a decimal, you might need to perform calculations with it. Decimal arithmetic follows the same basic rules as whole number arithmetic. However, the placement of the decimal point is crucial to getting the correct answer.

For addition or subtraction, line up the decimal points before carrying out the operation. When multiplying, count the total number of decimal places in the factors to determine where the decimal point should be in the product. With division, you may have to adjust the divisor and dividend to ensure a proper division process.

In the textbook problem, dividing 0.01 by 2 is an application of decimal arithmetic. Remember to keep the decimal point aligned and count the decimal places properly, so 0.01 divided by 2 gives the result of 0.005.

Critical to solving math problems is understanding the steps and the logic behind each one. Breaking down a problem into manageable parts and tackling each part methodically can simplify even the most complex problems.

Start by identifying what needs to be solved and clarifying any mathematical concepts involved, like percentage conversions in the textbook example. Next, apply appropriate math rules and operations step by step, monitoring your work to prevent small errors that could lead to incorrect answers. Finally, verify your results to confirm they make sense within the context of the problem.

For instance, after converting \( \frac{1}{2} \% \), to decimal 0.005, it's useful to consider whether this result aligns with the understanding that \( \frac{1}{2} \% \) is indeed a very small portion—smaller than 1%, and thus, the decimal equivalent should also be a small number that looks correct in this context.