Problem 62 - Prealgebra

Question

Write each decimal as an equivalent proper fraction or mixed number. 0.04

Step-by-Step Solution

Answer

0.04 is equivalent to \( \frac{1}{25} \).

Step 1: Understand the Decimal

The decimal number given is 0.04. We need to express this decimal as a fraction.

Step 2: Decimal to Fraction Representation

The decimal 0.04 translates to 4 hundredths, which can be written as the fraction \( \frac{4}{100} \).

Step 3: Simplify the Fraction

Find the greatest common divisor (GCD) of 4 and 100, which is 4. Divide both the numerator and denominator of \( \frac{4}{100} \) by 4. This results in \( \frac{1}{25} \).

Step 4: Verify the Fraction

The fraction \( \frac{1}{25} \) is in its simplest form because the GCD of 1 and 25 is 1. Thus, \( 0.04 = \frac{1}{25} \). It is a proper fraction since the numerator is less than the denominator.

Key Concepts

Understanding Proper Fractions

Proper fractions are a fundamental part of understanding fractions as a whole. A proper fraction is when the numerator, the top part of the fraction, is smaller than the denominator, the bottom part. This means that the fraction represents a quantity less than one whole unit.

For example, if we have a fraction like \( \frac{1}{25} \), it's considered a proper fraction because 1 (numerator) is less than 25 (denominator). This concept is important in decimal to fraction conversion because we need to make sure our final fraction accurately represents the value of the original decimal number.

Whenever you're working with fractions, keep in mind this simple idea: as long as the numerator remains smaller than the denominator, you're dealing with a proper fraction.

Simplifying Fractions: Making Things Easier

Simplifying fractions is a helpful process that makes them easier to work with. When we simplify a fraction, we're trying to find an equivalent fraction that has the smallest possible numerator and denominator without changing its value.

To do this, we divide both the numerator and the denominator by their greatest common divisor (GCD). Let's take our fraction \( \frac{4}{100} \) as an example.

• We determined that both 4 and 100 can be divided by 4, their GCD.
• By dividing both of these numbers by 4, we land on the simplified fraction \( \frac{1}{25} \).

Simplification is critical because it helps us to understand and work with fractions more smoothly. Always look for the GCD to simplify fractions as much as possible.

Greatest Common Divisor (GCD): The Simplifying Hero

The greatest common divisor (GCD) is a crucial mathematical tool when working with fractions. It refers to the largest number that can divide two or more numbers equally, without leaving a remainder.

Finding the GCD helps simplify fractions to their smallest form quickly and accurately. Here's how you can determine the GCD:

• List the factors of each number.
• Identify the largest factor that appears in both lists.

For our original fraction \( \frac{4}{100} \), we looked at the factors of 4 (1, 2, 4) and 100 (1, 2, 4, 5, 10, 20, 25, 50, 100). The highest common factor is 4, making it the GCD.

Using the GCD is key in converting any fraction to its simplest form, ensuring it is easy to interpret and work with. Remember, the GCD doesn't change the value of the fraction, just makes it simpler to manage.