Problem 26 - Prealgebra

Question

Estimate. Explain which method you used to estimate. $$\frac{1}{4} \% \text { of } 806$$

Step-by-Step Solution

Answer

Approximately 2. This was estimated using decimal conversion and rounding.

Step 1: Understand the Percentage

To estimate \( \frac{1}{4} \% \) of 806, we first recognize that \( \frac{1}{4} \% \) is equal to \( 0.25\% \). Thus, we need to find \( 0.25\% \) of the number 806.

Step 2: Convert Percentage to Decimal

Convert the percentage to a decimal for easier calculation. \( 0.25\% = \frac{0.25}{100} = 0.0025 \).

Step 3: Calculate the Estimated Value

To find \( 0.0025 \cdot 806 \), we perform the multiplication: \( 806 \times 0.0025 = 2.015 \).

Step 4: Round the Estimate

Since we are estimating, we can round our calculation to the nearest whole number. Therefore, \( 2.015 \) rounds to \( 2 \).

Key Concepts

Percentage Calculation

Calculating percentages involves understanding different parts of a whole. A percentage represents a fraction out of 100.

• Expressing as a fraction makes complex calculations simpler.
• For the problem \( \frac{1}{4}\% \), understand it as a fraction of a percent before moving forward.
• To break it down, \( \frac{1}{4}\% \) means "a quarter of a percent," translating to 0.25%.

This shows how percentages are flexible and often need to be broken down or converted to make calculations manageable.

Decimal Conversion

Converting percentages to decimals is a key step in many math problems. It simplifies calculations by changing percentages into a straightforward numeric form.

• To convert, divide the percentage by 100. For example, 0.25% becomes \( \frac{0.25}{100} \).
• The result is a decimal, straightforward to multiply with any given value.
• In the exercise, this conversion translates \( 0.25\% \) to \( 0.0025 \).

Decimals provide clarity, especially in multiplication tasks, and make the process less complex. Always ensure the conversion is accurate to avoid incorrect calculations.

Rounding Numbers

Rounding numbers helps to make figures easier to work with, especially in estimations. Once calculations are complete, round the number to an applicable degree of precision.

• In many cases, you round to the nearest whole number for simplicity.
• For example, from the result \( 2.015 \), rounding gives \( 2 \).
• Rounding doesn't just simplify numbers; it ensures clarity in communication.

The decision of how to round depends on the context. Adjust accordingly to either maintain precision or ease interpretation, especially when dealing with money or units where exact numbers matter less.