Problem 43 - Elementary Algebra

Question

Convert each percent to its decimal equivalent. $$ 0.025 \% $$

Step-by-Step Solution

Answer

0.025% converts to 0.00025 as a decimal.

Step 1: Understand the Percent

First, let's understand what the given percent means. Here, we have \(0.025\%\). Percent means per hundred.

Step 2: Convert Percent to Fraction

Since \(0.025\%\) means \(0.025\) out of 100, convert the percent to a fraction: \(\frac{0.025}{100}\).

Step 3: Simplify the Fraction

To convert \(\frac{0.025}{100}\) into a decimal, perform the division \(0.025 \div 100\). This can be simplified by moving the decimal two places to the left.

Step 4: Final Conversion

Perform the division or move the decimal point. \(0.025 \div 100 = 0.00025\).

Key Concepts

Percent to Decimal

When converting a percent to a decimal, remember that "percent" means "per hundred." This is a key concept to grasp. To convert any percentage to a decimal:

• Take the percent value.
• Divide it by 100.

To make calculations simpler, you can instead move the decimal point two places to the left. For example, converting \(0.025\%\) to a decimal:

• Move the decimal two spots to the left of \(0.025\), resulting in \(0.00025\).

This simple technique is handy and efficient, and it works for any percent value.

Fraction Simplification

Simplifying fractions is an essential skill that involves reducing fractions to their simplest form. In terms of percent conversion to decimals, the process involves using fractions less directly.When you convert \(0.025\%\) to a fraction, you start with \(\frac{0.025}{100}\). In many cases, it helps to simplify such expressions, but here simplification directly leads to decimal conversion:

• Perform the division \(0.025 \div 100\), which naturally simplifies in decimal form.

In practical terms, simplifying involves dividing both the numerator and the denominator by their greatest common factor (GCF), but with decimals, you might directly reach the decimal form instead.

Mathematical Operations

Basic mathematical operations such as division play a crucial role in converting percentages into decimals. Here's how you perform operations on the example \(0.025\%\):

• Start by framing it as a fraction, \(\frac{0.025}{100}\).
• To convert to a decimal, divide the numerator by the denominator.
• Here, \(0.025 \div 100 = 0.00025\).

Operations like division in this context are integral to simplifying and converting values efficiently. Understanding how to manipulate numbers this way enhances your capability to tackle varied mathematical tasks.