Conversion of Decimal Form into Rational Form
In mathematics, every decimal number can be expressed as a rational number (a fraction). This chapter explores the systematic methods for converting different types of decimals into their equivalent rational forms.
Types of Decimals
Decimals can be classified into two main categories:
Terminating Decimals
Repeating Decimals
Terminating Decimals: A terminating decimal is a decimal that ends after a finite number of digits. These decimals are the simplest to convert into fractions.
General Method:
Write the decimal as a numerator over a power of 10
Simplify the fraction by dividing both numerator and denominator by their greatest common factor (GCF)
Example:
To convert 0.625 to a fraction:
Repeating Decimals:
Repeating decimals have digits or groups of digits that repeat indefinitely. These require a more sophisticated approach for conversion.
Let's examine the process through an example.
For more complex repeating decimals like 0.272727...:
Important Notes
When writing repeating decimals, use a bar over the repeating portion (e.g., 0.2̅7̅)
Always verify your answer by dividing the numerator by the denominator.
Ensure your final answer is in simplified form.
Understanding these conversions is crucial for advanced mathematical concepts and real-world applications in fields such as engineering and science.