Problem 283 - Intermediate Algebra

Question

In the following exercises, convert each percent to \(a\) decimal. $$ 71 \% $$

Step-by-Step Solution

Answer

0.71

Step 1: Understanding Percent Conversion

To convert a percentage to a decimal, it’s important to understand that percent means 'per hundred.' This signifies that the given percentage is a fraction out of 100.

Step 2: Divide by 100

To convert 71% to a decimal, divide 71 by 100. This is because percent means per 100, so 71% is equivalent to \(\frac{71}{100}\).

Step 3: Perform the Division

Now, perform the division: \(\frac{71}{100} = 0.71\).

Key Concepts

percent

A percent represents a part of a whole, specifically out of 100. When you see a number followed by the percentage symbol (%), it means that number is out of 100. For example, 71% means 71 parts out of 100 parts. Understanding this concept is crucial because it forms the foundation for converting percentages to decimals. When you are asked to convert a percent to a decimal, remember that you are essentially finding how many parts per hundred the number represents.

decimal conversion

Decimal conversion involves turning a fraction or a percentage into a decimal number. This is a common procedure in math that helps simplify calculations and comparisons. In our problem, we need to convert 71% into a decimal. Since percent signifies 'out of 100', we begin by expressing 71% as a fraction: \( \frac{71}{100} \). Now, to convert this fraction to a decimal, you perform the division. Simply place 71 inside the division bracket and 100 outside, then divide to get the result: 0.71. So, 71% converted to a decimal is 0.71.

division

Division is the mathematical operation used to convert a percentage into a decimal. In the context of percent to decimal conversion, you always divide by 100. Let's break it down using our given number, 71%. To convert \( \frac{71}{100} \) into a decimal, you perform the division operation: \( 71 ÷ 100 = 0.71 \). This is always the case when converting percentages to decimals—divide the percentage number by 100, and the result is the decimal form. This simple division operation allows you to switch from the percent format to the decimal format effortlessly.