Problem 28 - Basic Engineering Mathematics

Question

Express 25 minutes as a percentage of 2 hours, correct to the nearest \(1 \%\).

Step-by-Step Solution

Answer

25 minutes is roughly 21% of 2 hours.

Step 1: Convert Time Units

To express 25 minutes as a percentage of 2 hours, we first need to have both quantities in the same unit. Since we want a percentage of hours, we convert 25 minutes to hours. There are 60 minutes in an hour, so: \[ \text{Hours} = \frac{25}{60} = 0.4167 \text{ hours} \].

Step 2: Set Up Fraction

Now, we set up a fraction with the converted amount of hours over the total hours: \[ \frac{0.4167 \text{ hours}}{2 \text{ hours}} \].

Step 3: Calculate the Percentage

To convert the fraction to a percentage, multiply by 100: \[ \left( \frac{0.4167}{2} \right) \times 100 \approx 20.835 \% \].

Step 4: Round the Percentage

Round the calculated percentage to the nearest percent. Here, 20.835% is rounded to 21%.

Key Concepts

Unit Conversion

Converting units is a crucial step in many mathematical problems, particularly when calculating percentages. In this exercise, we aim to express 25 minutes as a percentage of 2 hours, and for this, we need to convert time units so both quantities are in the same unit—typically hours.

To convert 25 minutes to hours, we use the understanding that 1 hour equals 60 minutes. Thus, we divide 25 by 60 to transform minutes into hours:

• Minutes converted to hours: \( \frac{25}{60} \approx 0.4167 \text{ hours} \)

This conversion allows us to work in a consistent unit system, simplifying percentage calculations down the line. Understanding how to convert between units is essential in various applications beyond this exercise, as it ensures accuracy and consistency in your results.

Fractions

Fractions represent parts of a whole and are integral to expressing relationships between quantities. To proceed with our percentage calculation, once we have our time in hours, we create a fraction.

• Our fraction consists of the part (0.4167 hours: the converted time) over the total (2 hours).
• This gives us: \( \frac{0.4167}{2} \).

Fractions are useful for comparisons and proportionality in various mathematical contexts. In this case, it visualizes how much 25 minutes "represents" in terms of the full 2-hour span. Mastering fractions leads to better comprehension of ratios and percentages, which are prevalent in everyday contexts like finance, science, and statistics.

Rounding Numbers

Rounding numbers is a valuable skill in mathematical calculations, ensuring simplicity and readability in results. After calculating the percentage, it's often necessary to round it to a suitable level of precision. In our exercise, the calculated percentage was approximately 20.835%.

• We round to the nearest integer, which in this case is 21%.

The rounding process involves examining the digit immediately following the target decimal place. If it's 5 or greater, we round up. Otherwise, we round down. Rounding effectively communicates values concisely, which is especially useful when clarity is desired without excessive detail. Understanding how and when to round can optimize data presentation in fields like economics and research.