.5625 as a fraction

Converting 0.5625 To A Fraction: A Step-By-Step Guide

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Converting decimals to fractions is a fundamental mathematical skill that enhances numerical comprehension and precision. Understanding how to express 0.5625 as a fraction involves a systematic approach to ensure accuracy.

Steps to Convert 0.5625 to a Fraction

  1. Express the Decimal as a Fraction:
    • Write 0.5625 as a fraction with 1 as the denominator: 0.56251\frac{0.5625}{1}
  2. Eliminate the Decimal Point:
    • Count the number of digits after the decimal point (four digits in this case).
    • Multiply both the numerator and the denominator by 10 raised to the power of the number of decimal places (10⁴ = 10,000): 0.5625×10,0001×10,000=5,62510,000\frac{0.5625 \times 10,000}{1 \times 10,000} = \frac{5,625}{10,000}
  3. Simplify the Fraction:
    • Determine the Greatest Common Divisor (GCD) of 5,625 and 10,000.
    • The GCD is 625.
    • Divide both the numerator and the denominator by the GCD: 5,625÷62510,000÷625=916\frac{5,625 \div 625}{10,000 \div 625} = \frac{9}{16}

Therefore, 0.5625 as a fraction in its simplest form is 916\frac{9}{16}.

Verification

To confirm the accuracy of the conversion, divide the numerator by the denominator: 9÷16=0.56259 \div 16 = 0.5625 This confirms that 916\frac{9}{16} is the correct fractional representation of 0.5625.

Conclusion

Converting the decimal 0.5625 to a fraction involves expressing it as 5,62510,000\frac{5,625}{10,000} and simplifying to 916\frac{9}{16}. Mastering this process enhances one’s ability to work seamlessly between decimal and fractional representations.

FAQ

  1. What is 0.5625 as a fraction?
    • 0.5625 as a fraction is 916\frac{9}{16}.
  2. How do you convert 0.5625 to a fraction?
    • Write 0.5625 as 0.56251\frac{0.5625}{1}, multiply numerator and denominator by 10,000 to get 5,62510,000\frac{5,625}{10,000}, then simplify to 916\frac{9}{16}.
  3. What is the GCD of 5,625 and 10,000?
    • The Greatest Common Divisor of 5,625 and 10,000 is 625.
  4. Can 0.5625 be expressed as a simple fraction?
    • Yes, 0.5625 simplifies to the fraction 916\frac{9}{16}.
  5. Why is it important to simplify fractions?
    • Simplifying fractions provides the most reduced form, making them easier to understand and work with in calculations.