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Understanding how to convert fractions into decimals is a crucial math skill that can simplify many problems involving numerical comparisons. To convert a fraction like \( \frac{1}{5} \) into a decimal, you simply divide the numerator (which is 1) by the denominator (which is 5).
Performing the operation \( 1 \div 5 \) gives us \( 0.2 \). This means that \( \frac{1}{5} \) is equivalent to \( 0.2 \) in decimal form.
By mastering this conversion, you can easily compare fractions with decimals or other fractions by having them in the same form. It is especially useful in problems that naturally mix fractions and decimals because it standardizes the way we understand these numbers, making mathematical operations and comparisons clearer and more straightforward.

When comparing decimals, it's important to examine each digit carefully from left to right. Decimals are essentially another way to express fractions, and they maintain the same basic principles when it comes to inequality comparisons.
In our original exercise, converting \( \frac{1}{5} \) to \( 0.2 \) allows us to directly compare the decimals \( 0.2 \) and \( 0.2 \).
Here’s how you can confidently compare decimals:

• Line up the decimal points.
• Compare digits from left to right.
• If the decimals are equal in every digit, they are equal numbers.

Understanding this can prevent mistakes, as visuals and approximations might lead to errors without proper step-by-step comparison.

Mathematical reasoning involves using logic to solve problems and justify your conclusions. In the case of inequalities, reasoning clearly and logically through each step is essential.
By converting \( \frac{1}{5} \) into a decimal, we arrive at \( 0.2 \). When asked to evaluate the inequality \( 0.2 \geq 0.2 \), we logically deduce that this is true, since a number is always equal to itself.
By applying reasoning, you ensure that:

• Each transformation or conversion step is valid.
• Comparisons are grounded in concrete mathematical properties.
• You reach correct conclusions by consistent and justified steps.

In solving any math problem, being methodical in reasoning helps not just in checking your work but also in building a solid understanding of larger mathematical concepts.