Problem 63 - Prealgebra

Question

Convert the given decimal to a fraction. Reduce your answer to lowest terms. 0.06

Step-by-Step Solution

Answer

The decimal 0.06 as a simplified fraction is \( \frac{3}{50} \).

Step 1: Understanding the Decimal

The decimal given is 0.06. Decimal numbers are based on powers of ten. Each digit to the right of the decimal point indicates a fraction of ten. Here, 0.06 means 6 hundredths.

Step 2: Write the Decimal as a Fraction

To convert the decimal 0.06 to a fraction, recognize that 0.06 is equivalent to 6/100 because the decimal 0.06 means 6 out of 100.

Step 3: Simplify the Fraction

The fraction 6/100 can be simplified by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 6 and 100 is 2. Divide both the numerator and the denominator by 2 to simplify the fraction: \( \frac{6}{100} = \frac{6\div2}{100\div2} = \frac{3}{50} \).

Key Concepts

Decimal Notation

Decimal notation is a way of representing numbers that uses a decimal point to separate the whole part from the fractional part. For example, in the number 0.06, 0 is the whole number and 06 is the part representing a fraction of a whole.

This system relies on powers of ten, meaning each digit in the fractional part represents a certain fraction of ten, hundred, thousand, and so on. Whenever you see a number like 0.06, think of it as

• 0 ones
• 6 hundredths

The position of the digits after the decimal point matters greatly. The first position is tenth, the second is hundredth, then thousandth, etc. Understanding this positional value notion helps in converting decimals to fractions effectively.

Simplifying Fractions

Simplifying fractions is the process of reducing a fraction to its simplest form. This means you make sure that the numerator (the top number) and the denominator (the bottom number) are as small as possible while still keeping the number equivalent.

For instance, if we start with the fraction 6/100 obtained from the decimal 0.06, we want to simplify it by dividing both the numerator and the denominator by the same number. Simplifying a fraction doesn't change its value; it only makes it easier to read and work with.

The ultimate aim is to reach a fraction where no number greater than 1 can divide both the numerator and the denominator. This often requires identifying a specific number called the greatest common divisor.

Greatest Common Divisor (GCD)

The greatest common divisor (GCD), also known as the greatest common factor, is an important concept for simplifying fractions. It's the largest number that can evenly divide both the numerator and the denominator of a fraction.

In the example of simplifying 6/100, the GCD is 2. This means 2 is the largest number that can divide both 6 and 100 evenly without leaving a remainder. By dividing both parts of the fraction by 2, you simplify 6/100 to 3/50.

Finding the GCD helps in reducing fractions effectively:

• List the factors of both numbers (e.g., 6 and 100).
• Identify the largest factor they have in common.
• Use it to divide both the numerator and the denominator.

This step is crucial if you want fractions that are easy to interpret and use in further calculations.