Converting decimals to fractions is a fundamental concept in mathematics, often required in various mathematical and real-world applications. The decimal 0.078125 is a specific value that can be converted into a fraction using straightforward mathematical techniques. In this article, we will explore how to convert 0.078125 to a fraction, providing a clear and simple solution.
Understanding Decimals and Fractions
Decimals and fractions are two different ways to represent parts of a whole. Decimals are based on the powers of ten, while fractions are based on the ratio of two integers. The decimal 0.078125 represents a small part of a whole, and converting it to a fraction provides an equivalent representation using integers.
Converting 0.078125 to a Fraction
To convert 0.078125 to a fraction, we can follow a simple process. First, we note that 0.078125 can be written as 78.125 / 1000. This fraction can then be simplified by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this GCD.
| Step | Value |
|---|---|
| Decimal | 0.078125 |
| Fraction | 78.125 / 1000 |
Simplification Process
The fraction 78.125 / 1000 can be simplified by first converting 78.125 to an integer fraction: 78.125 = 78 + 0.125 = 78 + 1⁄8 = 625⁄8. So, 78.125 / 1000 = (625⁄8) / 1000 = 625 / (8 * 1000) = 625 / 8000.
Now, we simplify 625 / 8000 by finding their GCD, which is 125. Dividing both the numerator and the denominator by 125 gives:
625 / 125 = 5
8000 / 125 = 64
So, 625 / 8000 simplifies to 5/64.
Verification
To verify that 5⁄64 is indeed equal to 0.078125, we can perform the division:
5 ÷ 64 = 0.078125
This confirms that our conversion is accurate.
Key Points
- The decimal 0.078125 can be converted to a fraction by expressing it as 78.125 / 1000.
- The fraction 78.125 / 1000 simplifies to 625 / 8000.
- Further simplification of 625 / 8000 yields 5/64.
- The fraction 5/64 is verified to be equal to 0.078125 through division.
- This process demonstrates a simple method for converting decimals to fractions.
Conclusion
In conclusion, the decimal 0.078125 converts to the fraction 5⁄64. This conversion was achieved by expressing the decimal as a fraction with a denominator that is a power of ten, and then simplifying the resulting fraction. Understanding how to convert between decimals and fractions is a valuable mathematical skill with numerous practical applications.
What is the simplest way to convert a decimal to a fraction?
+The simplest way is to express the decimal as a fraction with a denominator that is a power of ten and then simplify by finding the greatest common divisor (GCD) of the numerator and denominator.
How do I verify that a fraction is equal to a decimal?
+You can verify that a fraction is equal to a decimal by performing the division of the numerator by the denominator and comparing the result to the original decimal.
What is the fraction 5⁄64 in decimal form?
+The fraction 5⁄64 in decimal form is 0.078125.
