Converting decimals to fractions is a common and straightforward process that comes in handy when dealing with measurements, percentages, and everyday calculations. This guide will walk you through the simple steps to convert both simple and complex decimals into fractions, along with a few examples to make it easier to understand.
Why Convert Decimals to Fractions?
- Exact Values: Fractions can represent exact values, while decimals might sometimes round off. For example, the fraction 1/3 is an exact value, but its decimal equivalent (0.333…) is a repeating decimal.
- Simplifying Calculations: In some cases, using fractions can make calculations more manageable, especially when adding, subtracting, or multiplying numbers.
Basic Steps to Convert a Decimal to a Fraction
Step 1: Write Down the Decimal Divided by 1
Start by writing the decimal number as a fraction with 1 in the denominator.
For example, for the decimal 0.75:
Step 2: Multiply Both the Numerator and Denominator
If the decimal has digits after the decimal point, multiply both the numerator (top number) and the denominator (bottom number) by 10 for each digit after the decimal. This removes the decimal point.
For 0.75, there are two digits after the decimal, so multiply by 100:
Step 3: Simplify the Fraction
The last step is to simplify the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD).
For 75/100, the GCD of 75 and 100 is 25. Divide both the numerator and denominator by 25:
So, 0.75 as a fraction is 3/4.
Handling Different Types of Decimals
1. Terminating Decimals
These are decimals that come to an end (e.g., 0.5, 0.75, 0.125).
Example: Convert 0.5 to a fraction.
Step 1: Write as 0.5/1
Step 2: Multiply by 10 (since there’s 1 digit after the decimal):
Step 3: Simplify.
2. Repeating Decimals
These are decimals that repeat a specific digit or group of digits infinitely (e.g., 0.333…, 0.666…).
Example: Convert 0.333… to a fraction.
- Let (x = 0.333…).
- Multiply both sides by 10: (10x = 3.333…).
- Subtract (x) from (10x): (10x – x = 3.333… – 0.333…) resulting in (9x = 3).
- Divide by 9: 3/9.
- Simplify: 3/9 => 1/3.
Example Table of Decimal to Fraction Conversions
| Decimal | Fraction | Simplified Fraction |
|---|---|---|
| 0.25 | 25/100 | 1/4 |
| 0.5 | 5/10 | 1/2 |
| 0.75 | 75/100 | 3/4 |
| 0.2 | 2/10 | 1/5 |
| 0.125 | 125/1000 | 1/8 |
| 0.666… | 6/9 | 2/3 |
| 1.5 | 15/10 | 3/2 |
| 2.25 | 225/100 | 9/4 |
Quick Tips for Conversion
- Counting Decimal Places: The number of digits after the decimal point tells you how many zeros to place in the denominator (e.g., 0.25 has two digits after the decimal, so the denominator is 100).
- Repeating Decimals: For repeating decimals, use algebra to convert them to fractions (like the example with 0.333…).
- Simplify: Always simplify the fraction to its lowest terms for the final answer.
Practice Problems
Convert 0.6 to a fraction:
- Write as 6/10
- Multiply by 10: (6 / 10) * 10.
- Simplify to: 3/5.
Convert 0.875 to a fraction:
- Write as 0.8751/1.
- Multiply by 1000: 875/1000.
- Simplify to: 7/8.
Convert 1.75 to a fraction:
- Write as 1.75/1.
- Multiply by 100: 175/100.
- Simplify to: 7/4.
With practice, you’ll find that this process becomes quick and easy. Use the examples and tables provided to help with more complex conversions!