Problem 26 - Prealgebra

Question

Write each decimal as a fraction in lowest terms. $$0.06$$

Step-by-Step Solution

Answer

0.06 as a fraction in lowest terms is \( \frac{3}{50} \).

Step 1: Understand the Decimal

The given decimal is 0.06. This means it is 6 hundredths or 6 parts out of 100.

Step 2: Convert the Decimal to a Fraction

Write the decimal as a fraction. Since 0.06 is 6 hundredths, it can be written as \( \frac{6}{100} \).

Step 3: Simplify the Fraction

To simplify \( \frac{6}{100} \), find the greatest common divisor (GCD) of 6 and 100. The GCD of 6 and 100 is 2. Divide both the numerator and the denominator by 2: \( \frac{6 \div 2}{100 \div 2} = \frac{3}{50} \).

Step 4: Conclusion: Fraction in Lowest Terms

The fraction \( \frac{3}{50} \) cannot be simplified further. Thus, 0.06 as a fraction in lowest terms is \( \frac{3}{50} \).

Key Concepts

Simplifying Fractions

Simplifying fractions is like tidying up your room; it's about making things as simple as possible. A fraction becomes simplified when the numerator (the top number) and the denominator (the bottom number) have no common factors besides 1. This means you must divide both numbers by their greatest common divisor (GCD). This process reduces the fraction while keeping its value unchanged.

To simplify, start by identifying any common factors. For instance, in the fraction \( \frac{6}{100} \), the numbers 6 and 100 can both be divided by 2, their greatest common divisor. So, dividing each by 2 gives us \( \frac{3}{50} \). Since there are no other common factors, \( \frac{3}{50} \) is the simplified form.

Remember these key points:

• Identify the greatest common divisor of the numerator and denominator.
• Divide both numerator and denominator by the GCD.
• Check your work by ensuring no more common factors exist.

Practicing simplifying fractions helps you get comfortable with the process, much like uncongesting a jigsaw puzzle one piece at a time.

Fractions in Lowest Terms

Finding fractions in their lowest terms can make them easier to work with. A fraction is in its lowest terms when the numerator and the denominator are the smallest possible whole numbers, while still representing the same value of the fraction.

To achieve this, the simplifying fractions process is used. You repeatedly divide the numerator and the denominator by their common factors until none remain besides 1. For example, transforming \( \frac{6}{100} \) into \( \frac{3}{50} \) by dividing by 2 gives us its lowest terms representation. From here, computations with the fraction become simpler and clearer.

When fractions are in their lowest terms, they:

• Are less complex to reduce further.
• Represent the true portion or ratio succinctly.
• Make mathematical operations, such as adding or subtracting fractions, smoother.

If you ever get lost, remember just to break down the steps like decluttering your thoughts into the simplest form possible.

Greatest Common Divisor

The greatest common divisor (GCD) is a crucial player in simplifying fractions. Sometimes called the greatest common factor (GCF), it's the largest number that evenly divides both the numerator and the denominator without leaving a remainder.

Imagine the GCD as the greatest splitter of a faction's team; it helps to "divide and conquer" the common factors swiftly. To find it, you can:

• List all the divisors of each number.
• Identify the largest shared divisor.
• Use it to reduce the fraction to its simplest form.

In the example of \( \frac{6}{100} \), we find that 2 is the greatest number that both 6 and 100 can be divided by evenly. Therefore, 2 is the GCD.

Developing a knack for finding the GCD streamlines your ability to simplify fractions, making fraction work almost as sharp and precise as a pair of scissors cutting through paper. Anytime you want to simplify a fraction, just give a nod to your number-crunching companion, the GCD!