Konversi Desimal ke Pecahan Biasa: Panduan Lengkap

Converting decimal numbers to fractions might seem daunting at first, but it's a straightforward process once you understand the underlying principles. This guide will walk you through the steps involved in converting decimals to fractions, providing clear explanations and practical examples to solidify your understanding.

Decimals represent parts of a whole number, just like fractions. The key to converting decimals to fractions lies in recognizing the place value of each digit in the decimal. For instance, 0.5 represents half of a whole, which can be expressed as the fraction 1/2. Similarly, 0.25 represents one-quarter of a whole, which can be expressed as the fraction 1/4.

Understanding Place Value in Decimals

Before diving into the conversion process, it's crucial to understand the place value system in decimals. Each digit in a decimal holds a specific value based on its position relative to the decimal point. For example, in the decimal 0.345, the digit 3 represents three-tenths (3/10), the digit 4 represents four-hundredths (4/100), and the digit 5 represents five-thousandths (5/1000).

Converting Terminating Decimals to Fractions

Terminating decimals are decimals that end after a finite number of digits. Converting terminating decimals to fractions is a relatively simple process. Here's how:

1. Identify the place value of the last digit: Determine the place value of the last digit in the decimal. For example, in the decimal 0.75, the last digit (5) is in the hundredths place.

2. Write the decimal as a fraction: Write the decimal as a fraction with the decimal as the numerator and the place value as the denominator. In the example of 0.75, the fraction would be 75/100.

3. Simplify the fraction: Simplify the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor. In the example of 75/100, the greatest common factor is 25. Dividing both numerator and denominator by 25 gives us the simplified fraction 3/4.

Converting Repeating Decimals to Fractions

Repeating decimals are decimals that have a repeating pattern of digits after the decimal point. Converting repeating decimals to fractions requires a slightly different approach. Here's how:

1. Set up an equation: Let 'x' equal the repeating decimal. For example, if the repeating decimal is 0.3333..., then x = 0.3333...

2. Multiply both sides by 10: Multiply both sides of the equation by 10 raised to the power of the number of repeating digits. In the example of 0.3333..., we have one repeating digit, so we multiply both sides by 10. This gives us 10x = 3.3333...

3. Subtract the original equation: Subtract the original equation (x = 0.3333...) from the equation obtained in step 2 (10x = 3.3333...). This will eliminate the repeating decimal part. In our example, we get 9x = 3.

4. Solve for x: Solve the equation for 'x' by dividing both sides by 9. This gives us x = 1/3.

Conclusion

Converting decimals to fractions is a fundamental skill in mathematics, particularly when working with fractions and ratios. By understanding the place value system in decimals and applying the appropriate conversion methods, you can confidently convert any decimal to its equivalent fraction. Remember to simplify the fraction to its lowest terms for a more concise representation.