Problem 71 - Algebra A Combined Function

Question

Write each percent as a decimal. $$ 200 \% $$

Step-by-Step Solution

Answer

200% as a decimal is 2.

Step 1: Understand What Percent Means

A percent is a way of expressing a number as a fraction of 100. Specifically, "percent" means "per hundred." For example, 200% means 200 per 100.

Step 2: Convert Percent to a Fraction

To convert 200% to a fraction, we write it as \( \frac{200}{100} \). This represents the number 200 divided by 100.

Step 3: Simplify the Fraction

To simplify the fraction \( \frac{200}{100} \), we divide both the numerator and the denominator by their greatest common divisor, which is 100. This gives us \( 2 \), since \( \frac{200}{100} = 2 \).

Step 4: Convert the Simplified Fraction to a Decimal

The simplified fraction, \( 2 \), is already a decimal number. Therefore, the decimal equivalent of 200% is 2.

Key Concepts

Fractions

Fractions are a way to express numbers that are not whole numbers. They consist of two parts: a numerator and a denominator.
The numerator is the top part, while the denominator is the bottom. For example, in the fraction \( \frac{3}{4} \), 3 is the numerator and 4 is the denominator.
Fractions can represent parts of a whole. When the numerator is smaller than the denominator, it indicates a quantity smaller than one. When the numerator is larger, the fraction is greater than one.
Understanding fractions is crucial when working with percentages. Since percentages are a type of fraction (per hundred), converting between percentages and fractions involves a straightforward process:

• Write the percent as a fraction over 100.
• For example, 200% becomes \( \frac{200}{100} \).

This method seamlessly transitions you from percentages to fractions.

Simplifying Fractions

Simplifying fractions makes them easier to use and understand. A simplified fraction is one where the numerator and the denominator are reduced to their smallest possible values.To simplify a fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD).
Let's take the fraction \( \frac{200}{100} \). The GCD of 200 and 100 is 100.

Steps to Simplify

• Divide the numerator by 100: \( 200 \div 100 = 2 \).
• Divide the denominator by 100: \( 100 \div 100 = 1 \).
• You end up with \( \frac{2}{1} \), which simplifies to 2.

Simplified fractions are often easier to convert to decimals and easier to compare with other numerical forms.

Decimal Numbers

Decimals are numbers expressed in the base ten system. They are an alternative to fractions for representing parts of a whole.Decimals are especially useful because they align with our number system's structure, making calculations more streamlined.
For instance, the fraction \( \frac{1}{2} \) is equivalent to the decimal 0.5.

Converting Fractions to Decimals

For a fraction with a denominator of 1, such as \( \frac{2}{1} \), converting to a decimal is straightforward:

• Simply divide the numerator by the denominator: \( 2 \div 1 = 2 \).
• This shows that 200% becomes the decimal 2.

Decimals provide a clear and concise way to represent numbers, especially when dealing with percentages and simplified fractions.