Problem 47 - Elementary Algebra

Question

Convert each percent to its decimal equivalent. $$ 0 \% $$

Step-by-Step Solution

Answer

The decimal equivalent of 0% is 0.

Step 1: Understand the Problem

We are given a percentage: 0%. Our task is to convert this percentage into its decimal form.

Step 2: Review the Conversion Formula

Recall that to convert a percentage to a decimal, we divide the percentage value by 100. The formula is: \[ \text{Decimal} = \frac{\text{Percentage}}{100} \]

Step 3: Apply the Formula

Substitute the given percentage (0%) into the conversion formula: \[ \text{Decimal} = \frac{0}{100} \]

Step 4: Perform the Division

Perform the division: \( \frac{0}{100} = 0 \). Thus, the decimal equivalent of 0% is 0.

Key Concepts

Decimal Notation

In mathematics, decimal notation is a standard way to write numbers using a base of 10. It involves placing digits to the left and right of a decimal point. The numbers to the left are whole numbers, while those to the right represent fractions of ten. For example, the number 4.5 represents "four and a half," with 4 as the whole number and 5 as the tenth fraction.

Decimal notation is incredibly useful when converting measurements, doing simple arithmetic, and understanding fractional values. This is why it's important to convert percentages to decimal form. It helps to take portions of a whole and express them in a base-ten system, which is easier to work with in various mathematical calculations.

Percentage

A percentage is a value that represents a part out of 100. The word percentage comes from the Latin "per centum," meaning "by a hundred." We often see percentages in contexts like interest rates, discounts in shopping, and statistical reports. They are a simple way to convey proportions.

When we express a percentage, it highlights a specific part in relation to 100. For instance, 50% signifies 50 parts out of 100, or half. In practical terms, percentages allow easy comparison of relative sizes. By knowing how to convert these into decimals, we can switch to a mathematical format compatible with equations and calculations.

Division by 100

Converting a percentage to a decimal is straightforward once you grasp the concept of division by 100. When you have a percentage, you're basically expressing a ratio out of 100. Thus, dividing by 100 transforms this ratio into a decimal form.

For example, if you have 75% and you wish to convert it into a decimal, you divide 75 by 100:

• Set up the division: \( \frac{75}{100} \)
• Calculate: \( 0.75 \)

This method is foolproof for any percentage. By applying this to 0%, you divide 0 by 100, resulting in 0. This simple operation turns percentages into a form that is easier to use in everyday maths and scientific calculations.