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When you work with percentages, you're dealing with a part of 100. A percentage helps express how large or small a number is relative to 100. In our exercise, we are tasked with calculating a "fall" of a sewage pipe which is given as a percentage. Here's how you can make sense of percentage calculations easily.

Start by converting any mixed number percentage, like \( 2 \frac{1}{4}\% \), into an improper fraction. \( 2 \frac{1}{4} \) can be expressed as \( \frac{9}{4} \). This fraction tells you that for every 100 units measured, 9 of those are dedicated to the fall of the pipe.

To convert the percentage to a number that can easily be multiplied with other measurements, we transform it into a decimal. You do this by dividing by 100:

• Given fraction: \( \frac{9}{4} \).
• Divide \( \frac{9}{4} \) by 100 => \( \frac{9}{4} \div 100 = 0.0225 \).

This decimal form, 0.0225, represents the slope of the sewage pipe, making our calculations much easier to handle.

Fractions and decimals both represent parts of a whole, and converting between them is a fundamental skill in elementary algebra. In our exercise, we had to convert a percentage given in fractional form into a decimal to simplify calculations.

The percentage given was \( 2 \frac{1}{4}\% \). When converting, first turn any mixed percentage into an improper fraction. For \( 2 \frac{1}{4} \), you calculate as follows:

Multiply the whole number by the denominator, then add the numerator:

• 2 whole parts make \( 2 \times 4 = 8 \).
• Add 1 to get a numerator of 9, resulting in \( \frac{9}{4} \).

Next, divide the fraction by the percentage base, 100, to transform it into a decimal:

• \( \frac{9}{4} \div 100 = 0.0225 \).

This solution simplifies the percentage's role in further calculations, allowing for easier multiplication with other measurements.

In math, rounding simplifies numbers, making them easier to work with by approximating them to their nearest specified place value — such as whole numbers, tenths, or hundredths.

Our exercise required us to round the result to the nearest tenth, meaning we needed to focus on the first digit right after the decimal point. Here's how to round 1.0125 to achieve this:

Observe the hundredth place value, the second digit after the decimal:

• If it's 5 or higher, increase the tenth place by 1.
• If it's lower than 5, keep the tenth place the same.

Thus, with 1.0125, the number 1 in the "tenths" place stays the same since the subsequent digit (2) is less than 5. The rounded result is 1.0 feet.

Rounding helps deliver a comprehensible and neat result, essential in practical applications like our sewage pipe problem.