Decimals like 0.0625 are common in everyday calculations, but understanding their equivalent fractional form can make them easier to work with in various contexts. This guide will take you through the step-by-step process of converting 0.0625 to a fraction, simplifying it, and understanding its practical applications.

Step 1: Express 0.0625 as a Fraction

To convert a decimal to a fraction, start by expressing it as a fraction with a denominator of 1:

\[ 0.0625 = \frac{0.0625}{1} \]

Next, eliminate the decimal by multiplying both the numerator and denominator by \(10^4 = 10000\) (since there are four decimal places):

\[ \frac{0.0625 \times 10000}{1 \times 10000} = \frac{625}{10000} \]

Step 2: Simplify the Fraction

The fraction \(\frac{5}{80}\) can be further simplified. The GCD of 5 and 80 is 5. Divide both terms by 5:

The fraction \(\frac{625}{10000}\) can be simplified by finding the greatest common divisor (GCD) of 625 and 10000, which is 125. Divide both the numerator and denominator by 125:

The fraction \(\frac{5}{80}\) can be further simplified. The GCD of 5 and 80 is 5. Divide both terms by 5:

\[ \frac{5 \div 5}{80 \div 5} = \frac{1}{16} \]

Thus, 0.0625 is equal to the simplified fraction \(\frac{1}{16}\).

Understanding the Conversion

Converting 0.0625 to \(\frac{1}{16}\) highlights the relationship between decimals and fractions. In this case, the decimal 0.0625 represents 625 ten-thousandths, which simplifies to one-sixteenth.

Practical Applications

The fraction \(\frac{1}{16}\) appears in many real-world scenarios, such as:

  • Measurements: Common in ruler measurements, particularly in inches.
  • Cooking: Often used for precise ingredient quantities.
  • Mathematics: Simplifies ratio and proportion calculations.

Visualization of \(\frac{1}{16}\)

To visualize \(\frac{1}{16}\), imagine dividing a whole into 16 equal parts. Each part represents one-sixteenth of the whole, emphasizing the small size of the fraction.

Practice Problems

Test your understanding by converting these decimals into fractions:

  • 0.125
  • 0.375
  • 0.05

Conclusion

The decimal 0.0625 converts to the fraction \(\frac{1}{16}\) through a straightforward process of expressing it as a fraction and simplifying. Understanding these conversions is valuable in various practical applications, from cooking to engineering. By mastering this skill, you enhance your ability to work with numbers confidently.