Problem 175 Write each percent as a fraction... [FREE SOLUTION]

Chapter 0: Problem 175

Write each percent as a fraction. Give answers in lowest terms. See Example 13. $$ 2 \% $$

Short Answer

Expert verified

2% as a fraction in lowest terms is $ \frac{1}{50} $.

Step by step solution

Understand the Percent

The first step is to understand that the percent symbol '%' means 'per hundred'. Therefore, 2% can be written as 2 per 100 or as a fraction: $ \frac{2}{100} $.

Simplify the Fraction

To simplify the fraction $ \frac{2}{100} $, we need to find the greatest common divisor (GCD) of 2 and 100. The GCD of 2 and 100 is 2. Next, divide the numerator and the denominator by the GCD: $ \frac{2 \div 2}{100 \div 2} = \frac{1}{50} $.

Confirm the Simplified Fraction

Check that $ \frac{1}{50} $ is in its lowest terms. Since 1 and 50 have no common factors other than 1, the fraction $ \frac{1}{50} $ is already in its simplest form.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percent to Fraction Conversion

Converting percentages to fractions is a common task in mathematics. A percent represents a part out of 100. For example, 2% means 2 out of 100. Therefore, to convert a percent into a fraction, you place the percentage number over 100.

It's that easy! So, 2% becomes $ \frac{2}{100} $.

Remember, this step is just the beginning. While $ \frac{2}{100} $ is correct, it's not in its simplest form. Now, we need to simplify this fraction.

Greatest Common Divisor (GCD)

To simplify a fraction, we use the greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both of them without leaving a remainder.

For the fraction $ \frac{2}{100} $, we need to find the GCD of 2 and 100.

Let's break it down:

The factors of 2 are 1 and 2.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

The largest common factor is 2, so the GCD of 2 and 100 is 2. This means we can divide both the numerator (top number) and the denominator (bottom number) by 2 to simplify the fraction.

Simplification of Fractions

Now that we have the GCD, it's time to simplify $ \frac{2}{100} $. We do this by dividing both the numerator and the denominator by their GCD (which is 2).

When we divide 2 by 2, we get 1. When we divide 100 by 2, we get 50. So, $ \frac{2}{100} $ simplifies to $ \frac{1}{50} $.

Let's check if $ \frac{1}{50} $ is in its lowest terms: The only common factor of 1 and 50 is 1, which means $ \frac{1}{50} $ is indeed in its simplest form.

And that's it! We've taken 2%, converted it to the fraction $ \frac{2}{100} $, found the GCD of 2 and 100, and then simplified to get $ \frac{1}{50} $.

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91影视

Write each percent as a fraction. Give answers in lowest terms. See Example 13. $$ 2 \% $$

Short Answer

Step by step solution

Understand the Percent

Simplify the Fraction

Confirm the Simplified Fraction

Key Concepts

Percent to Fraction Conversion

Greatest Common Divisor (GCD)

Simplification of Fractions

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