Problem 65 - 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 the Concept of Percent

A percent is a ratio expressed out of 100. So, 200% is equivalent to 200 out of 100.

Step 2: Convert Percent to Fraction

To convert percent to a fraction, divide the percent value by 100. Therefore, 200% becomes \( \frac{200}{100} \).

Step 3: Simplify the Fraction

Simplify \( \frac{200}{100} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 100. This gives us \( 2 \).

Step 4: Write the Simplified Fraction as a Decimal

Since \( \frac{200}{100} = 2 \), and 2 is already a decimal. Hence, 200% as a decimal is 2.

Key Concepts

Understanding Percents

Percents are a way to express numbers as parts of a whole, described in terms of 100. When you see a percentage, it tells you how many parts out of 100 you have. This makes it simpler to compare different quantities: a straightforward, universally understood language.
Consider 200%. This means you have 200 out of 100 equal parts. Yes, 200 out of 100 might sound odd, but it shows that you have twice as much as the whole.

• Think of pouring water into a glass. If 100% is a full glass, 200% means you've filled it up twice.
• This method is useful in various applications, like increase in salary, where 200% could mean doubling your initial pay.

Percentages simplify comparisons, showing proportional relationships intuitively and dynamically.

Fractions

Fractions are another key concept to understand when converting percents to decimals. A fraction represents the division of one quantity by another. It consists of a numerator (the top number) and a denominator (the bottom number).

When dealing with percents, you convert them into fractions by placing the percent number over 100.

Converting Percent to Fraction

Starting with 200%, you make it a fraction:

• You write it as \( \frac{200}{100} \).

This is because the 'per cent' literally means 'per one hundred'. So every percentage can straightaway be written as a fraction out of 100.

Simplifying the Fraction

Next, you simplify \( \frac{200}{100} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 100.

• This yields the fraction \( \frac{2}{1} \).
• An easier way to look at this: 200 divided by 100 equals 2.

Fractions pave the way to decimals, simplifying processes while maintaining accurate relationships between numbers.

Decimal Representation

Decimals are a way of expressing fractions in a base ten system, utilizing a decimal point to separate the whole number from the fractional part. They offer an alternative, often more intuitive representation of fractions.

From Fraction to Decimal

Once you have simplified a fraction like \( \frac{2}{1} \), converting it to a decimal is straightforward. Since the numerator 2 is divisible by 1 with no remainder, the decimal representation remains 2.

• This understanding makes converting larger percents to decimals seamless.
• By turning complicated fractions into understandable decimals, calculations become easier.

Decimals help in expressing numbers in a format that's easy to interpret, making them useful in many real-world contexts like money, measurements, and statistics. This simplification is crucial in everyday calculations, providing a quicker and more efficient means to convey mathematical information.