The decimal value.8 can be converted into a fraction by considering it as 8/10, which can then be simplified. To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD), which in this case is 2.
Step-by-Step Simplification
First, identify the GCD of 8 and 10. The factors of 8 are 1, 2, 4, 8, and the factors of 10 are 1, 2, 5, 10. The greatest common factor they share is 2.
Calculating the Simplified Fraction
Divide both the numerator (8) and the denominator (10) by the GCD (2) to simplify the fraction.
| Original Fraction | Numerator | Denominator | GCD |
|---|---|---|---|
| 8/10 | 8 | 10 | 2 |
| Simplified Fraction | 8 / 2 = 4 | 10 / 2 = 5 |
This simplification results in the fraction 4/5, which is the fractional representation of the decimal.8.
Key Points
- The decimal.8 is equivalent to the fraction 8/10.
- Simplifying 8/10 by dividing both the numerator and denominator by their greatest common divisor (2) yields 4/5.
- The fraction 4/5 is the simplest form of.8 as a fraction.
- This conversion is essential in mathematics for understanding the relationship between decimals and fractions.
- Fractions like 4/5 are used in various mathematical operations and real-world applications.
Conclusion and Further Considerations
In conclusion, converting the decimal.8 to a fraction results in 4⁄5. This understanding is crucial for performing mathematical operations that require fractions and for applying mathematical concepts to real-world problems. The process of converting decimals to fractions involves identifying the place value of the decimal and then simplifying the resulting fraction, if possible.
What is the greatest common divisor (GCD) of 8 and 10?
+The GCD of 8 and 10 is 2, as it is the largest number that divides both 8 and 10 without leaving a remainder.
How do you simplify a fraction?
+To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). This process reduces the fraction to its simplest form while maintaining its value.
What are the real-world applications of converting decimals to fractions?
+Converting decimals to fractions has numerous real-world applications, including measurement conversions, financial calculations, and scientific computations, where precise fractional representations are necessary for accuracy and understanding.
