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Decoding Decimal into Fraction: Understanding the Representation of .6875 as a Fraction

Introduction

The decimal representation 0.6875 may seem like a straightforward number, but understanding it as a fraction can shed light on its precise mathematical value. In this exploration, we will break down the process of converting 0.6875 into a fraction step by step, providing comprehensive insights and additional information to enhance mathematical understanding.

Understanding Decimal Notation

Decimal notation, such as 0.6875, is a system where numbers are expressed in base-10 with a decimal point separating the whole and fractional parts. Breaking down the components of the decimal aids in unraveling its fractional equivalent.

Step-by-Step Conversion

To convert 0.6875 into a fraction, begin by understanding the decimal place value. In this case, the digit ‘6’ is in the tenths place, ‘8’ in the hundredths place, ‘7’ in the thousandths place, and ‘5’ in the ten-thousandths place. Each digit contributes to a power of 10 in the fractional representation.

Expressing Each Decimal Place as a Fraction

Assigning each digit its corresponding fractional value, the process involves expressing ‘6’ as 610, ‘8’ as 8100, ‘7’ as 71000, and ‘5’ as 510000.

Combining Fractional Parts

Combining these fractional parts gives 610+8100+71000+510000. The next step involves finding a common denominator to simplify the expression.

Simplifying the Fraction

The common denominator for 10, 100, 1000, and 10000 is 10000. Adjusting the fractions accordingly, we get 600010000+80010000+7010000+510000.

Combining and Simplifying Further

Consolidating the numerators results in 687510000, which can be further simplified by dividing both the numerator and denominator by their greatest common factor, 125.

Final Fractional Representation

The simplified fraction is 5580, representing the decimal 0.6875 in fractional form.

Additional Information

  • Equivalent Fractions: Explore other equivalent fractions of 5580, such as 1116 or 3348, showcasing the flexibility of fractional representation.
  • Decimal to Fraction Conversion Chart: Visualize the conversion process with a chart, illustrating the decimal digits and their fractional equivalents.

Conclusion

Converting 0.6875 into a fraction involves a step-by-step process, emphasizing the significance of decimal place values and fractional representations. The final fraction, 5580, encapsulates the original decimal in a concise and equivalent mathematical form. Utilizing this knowledge enhances numerical comprehension and provides a foundation for further mathematical exploration.

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