Converting 0.6875 To A Fraction: A Step-By-Step Guide

Converting decimals to fractions is a fundamental mathematical skill. Understanding how to express 0.6875 as a fraction can enhance your numerical proficiency and is applicable in various real-world scenarios.

Understanding Decimal to Fraction Conversion

A decimal represents a part of a whole number, and converting it to a fraction involves expressing that part as a ratio of two integers. The process includes identifying the place value of the decimal and simplifying the resulting fraction.

Steps to Convert 0.6875 to a Fraction

  1. Express the Decimal as a Fraction: Write 0.6875 as a fraction with 1 as the denominator: 0.68751\frac{0.6875}{1}10.6875​
  2. Eliminate the Decimal Point: Count the number of decimal places in 0.6875, which is four. Multiply both the numerator and the denominator by 10 raised to the power of the number of decimal places (10⁴ = 10,000): 0.6875×10,0001×10,000=6,87510,000\frac{0.6875 \times 10,000}{1 \times 10,000} = \frac{6,875}{10,000}1×10,0000.6875×10,000​=10,0006,875​
  3. Simplify the Fraction: Determine the greatest common divisor (GCD) of 6,875 and 10,000, which is 625. Divide both the numerator and the denominator by their GCD: 6,875÷62510,000÷625=1116\frac{6,875 \div 625}{10,000 \div 625} = \frac{11}{16}10,000÷6256,875÷625​=1611​

Therefore, 0.6875 as a fraction in its simplest form is 1116\frac{11}{16}1611​.

Verification

To confirm the accuracy, divide 11 by 16: 11÷16=0.687511 \div 16 = 0.687511÷16=0.6875 This confirms that 1116\frac{11}{16}1611​ is the correct fractional representation of 0.6875.

Applications of Converting Decimals to Fractions

Understanding how to convert decimals to fractions is useful in various fields, including:

  • Cooking: Adjusting ingredient measurements.
  • Construction: Interpreting measurements and dimensions.
  • Finance: Calculating interest rates and financial ratios.

Conclusion

Converting 0.6875 to a fraction involves expressing it as 6,87510,000\frac{6,875}{10,000}10,0006,875​ and simplifying to 1116\frac{11}{16}1611​. Mastering this process enhances numerical literacy and is applicable in everyday situations.

FAQ

  1. What is 0.6875 as a fraction?
    0.6875 as a fraction in simplest form is 1116\frac{11}{16}1611​.
  2. How do you convert a decimal to a fraction?
    Write the decimal as a fraction with 1 as the denominator, eliminate the decimal by multiplying by a power of 10, and simplify the fraction.
  3. Why is it important to simplify fractions?
    Simplifying fractions makes them easier to understand and use in calculations.
  4. Can all decimals be converted to fractions?
    Yes, all terminating and repeating decimals can be expressed as fractions.
  5. What is the GCD, and why is it used in simplifying fractions?
    The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator without a remainder, used to simplify fractions to their lowest terms.




    Take a look at this interesting piece blue-flowers-aand-their-meanings