Problem 11 - Prealgebra

Question

Change each percent to a decimal. $$92 \%$$

Step-by-Step Solution

Answer

92% as a decimal is 0.92.

Step 1: Understand Percent to Decimal Conversion

Percent means 'per hundred', so to convert a percentage to a decimal, divide the percentage by 100. This operation shifts the decimal point two places to the left.

Step 2: Apply the Conversion Formula

Take the given percentage \(92\%\) and divide by 100: \[92\% = \frac{92}{100}\]. This is the basic conversion method for turning a percent into a decimal.

Step 3: Shift the Decimal Point

Shifting the decimal point two places to the left for \(92\) gives us \[0.92\]. This is the decimal equivalent of \(92\%\).

Key Concepts

Converting Percentages

Percentages represent a number out of 100, simplifying comparisons and calculations. But, often in math, using decimals makes calculations easier. Converting percentages to decimals is a fundamental skill, especially in various math problems. Here's how to do it:

• Recognize that "per cent" means "per hundred." Therefore, 50% is the same as saying 50 out of 100.
• For the conversion, simply divide the percentage by 100 or shift the decimal point two places to the left.
• For example, converting 20% to a decimal involves moving the decimal point from after the zero to before the two, resulting in 0.20.

When you understand these basics, you can apply this to any percentage value, simplifying the process of dealing with various numbers in math.

Decimals in Math

Decimals are numbers expressed in a base ten system, which makes them extremely useful in everyday life and in mathematics for precise calculations. In the context of converting percentages to decimals, they help shed light on the true size of a percentage. A team of numbers, decimals help you perform arithmetic operations such as addition and subtraction with fractions, providing a common ground for comparison. Their placement is pivotal:

• The number to the left of the decimal mark is the whole number.
• The figures to the right represent parts of that whole—a tenth, a hundredth, and so on.

When correctly understood, decimals translate complex data into simpler, easily comparable formats.

Mathematical Operations

Mathematical operations include four primary activities: addition, subtraction, multiplication, and division. Each of these can be directly applied to decimals, including those converted from percentages, to solve real-world problems. Using decimals has advantages:

• Addition/Subtraction: Align decimals points before performing the operation, ensuring accuracy.
• Multiplication: Multiply as you would whole numbers and then count decimal places from both factors to place your decimal in the product.
• Division: If dividing by a decimal, shift the decimal place to create a whole number, adjusting the dividend's decimal place similarly.

These operations are foundational skills, enabling you to manipulate and solve problems involving decimals from percentages effectively.