Problem 68 - Algebra 1

Question

PERCENTS AS DECIMALS Write the percent as a decimal. $$ 87.5 \% $$

Step-by-Step Solution

Answer

The decimal form of 87.5% is 0.875.

Step 1: Understand the conversion

It's important to know that converting a percent into a decimal involves dividing the percent value by 100. This operation effectively moves the decimal point two places to the left.

Step 2: Apply the conversion

The value that is needed to be converted is 87.5%. To obtain the decimal form, divide 87.5 by 100. This can be done by simply moving the decimal two places to the left, resulting in 0.875.

Key Concepts

Mathematical Operations

When converting percentages to decimals, mathematical operations play a crucial role. The primary operation involved here is division. When you have a percentage, this number is typically out of 100. To convert a percentage to a decimal, you simply divide by 100. This can look intimidating if you're not familiar, but it's quite straightforward! To see this in action, take **87.5%** as an example. In mathematical terms, this is written as:\[ \frac{87.5}{100} \]When you perform this division, it results in 0.875.Using this method consistently can help you tackle any percentage to decimal conversion you encounter. Despite the simplicity, it's a fundamental part of handling percentages and understanding how they relate to other numeric formats.

Decimal Notation

Decimal notation is a way of writing numbers that uses a decimal point to separate the whole number part from the fractional part. Understanding decimal notation is essential when converting percentages to decimals because it helps in visualizing where to place the decimal point. When we convert **87.5%** to a decimal, we apply the principle that the percent means 'per hundred.' By dividing by 100, as explained earlier, we move the decimal point two places to the left. Hence, 87.5% becomes 0.875 in decimal notation. To simplify:

• Numbers to the left of the decimal point represent whole units.
• Numbers to the right represent parts of a unit.

This shift is a simple yet powerful way to represent parts of numbers and is crucial in fields such as science and statistics.

Understanding Percentages

Percentages are a way to express numbers as a fraction of 100. In daily life, percentages are everywhere, from discounts in shopping to statistics in studies. They offer an intuitive way of understanding proportions and ratios. To convert percentages like **87.5%** to their decimal equivalents, it's crucial to understand that the percent symbol (%) signifies a fraction out of 100. This is why the decimal form represents the exact part of 100 we are dealing with; here, it is 0.875. Knowing how to quickly move between these two representations—percent and decimal—enhances numerical literacy and provides immense flexibility in mathematical reasoning.