Unraveling the Numerical Expression
1. Introduction to Decimal Representation
In the realm of mathematics, decimals offer a precise way to express fractional values in a numerical format. The decimal .6875, while seemingly complex, can be systematically converted into a fraction, providing a clearer understanding of its fractional equivalent.
2. Decimal to Fraction Conversion: The Step-by-Step Process
To convert .6875 into a fraction, we follow a systematic process. Begin by identifying the place value of each digit after the decimal point. In the case of .6875, the digit 6 is in the tenths place, 8 is in the hundredths place, 7 is in the thousandths place, and 5 is in the ten-thousandths place.
3. Understanding the Decimal Places
In .6875, the decimal places signify the fractional parts. The digit 6 in the tenths place represents 6/10, the digit 8 in the hundredths place represents 8/100, the digit 7 in the thousandths place represents 7/1000, and the digit 5 in the ten-thousandths place represents 5/10,000.
4. Expressing Each Decimal Place as a Fraction
Breaking down the decimal into fractional components, we have:
- The tenths place, 6/10
- The hundredths place, 8/100
- The thousandths place, 7/1000
- The ten-thousandths place, 5/10,000
5. Combining Fractional Components .6875 as a Fraction
To find the overall fraction, combine these fractional components. Thus, .6875 as a fraction can be expressed as (6/10) + (8/100) + (7/1000) + (5/10,000).
6. Simplifying the Fraction
To simplify the expression, find a common denominator. In this case, the common denominator is 10,000. Adjust each fractional component accordingly. The resulting expression is (6000/10,000) + (800/10,000) + (7/1000) + (5/10,000).
7. Combining Numerators
Combine the numerators, resulting in the expression (6000 + 800 + 7 + 5)/10,000.
8. Final Simplification .6875 as a Fraction
Summing up the numerators (6000 + 800 + 7 + 5) yields 6820. Therefore, the fraction equivalent of .6875 is 6820/10,000.
9. Reducing the Fraction
To further simplify, find the greatest common factor (GCF) of the numerator and denominator, which is 20. Dividing both by 20 results in the simplified fraction 341/500.
10. Conclusion: .6875 as the Fraction 341/500
In conclusion, the decimal .6875 can be expressed as the simplified fraction 341/500. Understanding the step-by-step process of converting decimals to fractions enhances mathematical comprehension and facilitates accurate representation of numerical values in fractional form.
