Problem 7 - Prealgebra

Question

Express each percent as a fraction or mixed number in simplest form and as a decimal. $$0.2 \%$$

Step-by-Step Solution

Answer

0.2% as a fraction is \( \frac{1}{500} \) and as a decimal is 0.002.

Step 1: Convert Percent to Fraction

Percent means per hundred, so 0.2% can be expressed as a fraction: \( \frac{0.2}{100} \).

Step 2: Simplify the Fraction

To simplify \( \frac{0.2}{100} \), it's easier if we first deal with whole numbers. Multiply the numerator and the denominator by 10 to eliminate the decimal: \( \frac{2}{1000} \). Now, simplify by finding the greatest common divisor (GCD), which is 2. Divide both the numerator and the denominator by 2: \( \frac{1}{500} \).

Step 3: Convert to Decimal

To convert \( \frac{1}{500} \) to a decimal, divide 1 by 500. This gives 0.002.

Key Concepts

Simplifying Fractions

Simplifying fractions means reducing them to their smallest possible form. Fractions consist of a numerator and a denominator. The process involves finding a common number that can evenly divide both the numerator and the denominator.When we talk about simplifying, we mean dividing both parts of the fraction by their greatest common divisor (GCD). For example, in the solution given, we started with the fraction \( \frac{2}{1000} \). The most efficient way to simplify it is to find the GCD, which in this case is 2. By dividing both the numerator and the denominator by 2, we get \( \frac{1}{500} \).

• Step 1: Find the GCD of the numerator and the denominator.
• Step 2: Divide both the numerator and the denominator by the GCD.
• Step 3: Verify the fraction cannot be simplified further.

By ensuring fractions are in their simplest form, you make them easier to work with and understand. It also helps in making accurate comparisons between different fractions.

Decimal Conversion

Converting fractions to decimals is a fundamental skill in prealgebra. This involves division, where the numerator is divided by the denominator.Consider our simplified fraction \( \frac{1}{500} \). To convert it to a decimal, perform 1 divided by 500. This results in 0.002.

• Always divide the numerator by the denominator to find the decimal equivalent.
• You can use long division or a calculator for accurate results.
• Remember that some fractions may give a repeating or terminating decimal.

The skill of decimal conversion is useful for practical applications, such as financial calculations, measurements, and more. It helps in precisely representing values that are easier to work with in real-world contexts.

Prealgebra Concepts

Prealgebra lays the foundation for all higher levels of mathematics. It involves understanding basic arithmetic, fractions, decimals, and percentages.In the given exercise, we converted a percent to a fraction and then to a decimal, which encompasses several prealgebra skills. Here’s a quick recap:

• Understanding percentages and their representation as \( \frac{\text{part}}{100} \).
• Converting mixed numbers and decimals to simpler forms like fractions.
• Ensuring accuracy in calculations by practicing operations like division and multiplication within a fraction context.

Strengthening these prealgebra skills is crucial, as they are the building blocks for tackling complex algebraic concepts. They provide a solid understanding to successfully manage everyday numerical and quantitative challenges.