How to Turn a Decimal into a Fraction: A Simple Guide
Turning a decimal into a fraction might seem daunting, but it's a straightforward process once you understand the steps. This guide will walk you through different methods, ensuring you can confidently convert any decimal into its fractional equivalent. We'll cover both terminating and repeating decimals.
Understanding Decimals and Fractions
Before we dive into the conversion process, let's refresh our understanding of decimals and fractions. A decimal represents a part of a whole number using a base-ten system, separated by a decimal point. A fraction, on the other hand, represents a part of a whole number as a ratio of two integers – a numerator (top number) and a denominator (bottom number).
Method 1: Converting Terminating Decimals to Fractions
Terminating decimals are decimals that end after a finite number of digits (e.g., 0.75, 0.25, 0.5). These are the easiest to convert.
Steps:
-
Write the decimal as a fraction with a denominator of 1: For example, 0.75 becomes 0.75/1.
-
Multiply both the numerator and denominator by a power of 10 to eliminate the decimal point. The power of 10 will depend on the number of digits after the decimal point. For 0.75 (two digits after the decimal), multiply by 100: (0.75 x 100) / (1 x 100) = 75/100.
-
Simplify the fraction: Find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. The GCD of 75 and 100 is 25. Dividing both by 25 gives us 3/4.
Example: Convert 0.25 to a fraction.
- 0.25/1
- (0.25 x 100) / (1 x 100) = 25/100
- Simplify: 25/100 = 1/4
Example: Convert 0.625 to a fraction.
- 0.625/1
- (0.625 x 1000) / (1 x 1000) = 625/1000
- Simplify: 625/1000 = 5/8
Method 2: Converting Repeating Decimals to Fractions
Repeating decimals are decimals with a digit or sequence of digits that repeat infinitely (e.g., 0.333..., 0.142857142857...). Converting these requires a slightly different approach.
Steps:
-
Let x equal the repeating decimal: For example, if the decimal is 0.333..., let x = 0.333...
-
Multiply x by a power of 10 that shifts the repeating part to the left of the decimal point. For 0.333..., multiply by 10: 10x = 3.333...
-
Subtract the original equation (x) from the new equation (10x): 10x - x = 3.333... - 0.333... This simplifies to 9x = 3.
-
Solve for x: Divide both sides by 9: x = 3/9.
-
Simplify the fraction: 3/9 simplifies to 1/3.
Example: Convert 0.142857142857... to a fraction.
- Let x = 0.142857142857...
- Multiply by 1,000,000 (because there are six repeating digits): 1,000,000x = 142857.142857...
- Subtract: 1,000,000x - x = 142857
- 999,999x = 142857
- x = 142857/999999
- Simplify: x = 1/7
Tips for Success
- Practice makes perfect: The more you practice, the easier it will become.
- Use a calculator: A calculator can help simplify fractions quickly.
- Double-check your work: Always verify your answer to ensure accuracy.
By following these methods, you can confidently convert decimals into fractions, enhancing your mathematical skills and understanding. Remember to always simplify your final fraction to its lowest terms.
