Understanding the Concept of Converting Decimal to Fraction
The process of converting a decimal to a fraction involves several steps to ensure the conversion is accurate and straightforward. Here's a detailed guide to help you understand this process.
Step 1: Identify the Decimal
First, look at the decimal you need to convert. For example, let's consider the decimal 0.75.
Step 2: Place the Decimal over 1
Next, write the decimal number over 1. This creates a fraction:
$\frac{0.75}{1}$
Step 3: Eliminate the Decimal Point
To eliminate the decimal point, multiply both the numerator and the denominator by a power of 10 that converts the decimal to a whole number. For 0.75, multiply by 100:
$\frac{0.75 \times 100}{1 \times 100} = \frac{75}{100}$
Step 4: Simplify the Fraction
Now, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this number. The GCD of 75 and 100 is 25:
$\frac{75 \div 25}{100 \div 25} = \frac{3}{4}$
So, 0.75 converts to the fraction $\frac{3}{4}$.
Step 5: Verify the Conversion
Finally, check your work by converting the fraction back into a decimal. Divide the numerator by the denominator:
$\frac{3}{4} = 0.75$
Example
Let's do another example with the decimal 0.125.

Place the decimal over 1:
$\frac{0.125}{1}$

Eliminate the decimal by multiplying by 1000 (since there are 3 decimal places):
$\frac{0.125 \times 1000}{1 \times 1000} = \frac{125}{1000}$

Simplify the fraction by finding the GCD of 125 and 1000, which is 125:
$\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}$
So, 0.125 converts to the fraction $\frac{1}{8}$.
Summary
By following these steps, any decimal can be successfully converted into a fraction. The key points include identifying the decimal, eliminating the decimal point by multiplying, and simplifying the fraction. Practice will help you become more proficient at converting decimals to fractions.