Understanding how to convert decimals to fractions is a fundamental mathematical skill. In this guide, we’ll focus on converting the decimal 0.8125 into its simplest fractional form.
Step 1: Express the Decimal as a Fraction
To begin, write 0.8125 as a fraction with 1 as the denominator:
0.8125=0.812510.8125 = \frac{0.8125}{1}0.8125=10.8125
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Step 2: Eliminate the Decimal Point
Since 0.8125 has four digits after the decimal point, multiply both the numerator and the denominator by 10,000 to remove the decimal:
0.8125×10,0001×10,000=8,12510,000\frac{0.8125 \times 10,000}{1 \times 10,000} = \frac{8,125}{10,000}1×10,0000.8125×10,000=10,0008,125
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Step 3: Simplify the Fraction
To simplify, find the greatest common divisor (GCD) of 8,125 and 10,000. The GCD is 625. Divide both the numerator and the denominator by 625:
8,125÷62510,000÷625=1316\frac{8,125 \div 625}{10,000 \div 625} = \frac{13}{16}10,000÷6258,125÷625=1613
Therefore, 0.8125 as a fraction in its simplest form is 13/16.
Verification
To confirm the accuracy, divide 13 by 16:
13÷16=0.812513 \div 16 = 0.812513÷16=0.8125
This confirms that our conversion is correct.
Understanding the Process
Converting a decimal to a fraction involves:
- Writing the decimal as a fraction with the decimal number as the numerator and 1 as the denominator.
- Eliminating the decimal point by multiplying both the numerator and the denominator by a power of 10 equal to the number of decimal places.
- Simplifying the fraction by dividing both the numerator and the denominator by their GCD.
FAQ
- Why multiply by 10,000 in Step 2?
Multiplying by 10,000 shifts the decimal point four places to the right, converting 0.8125 to 8,125. - How is the GCD determined?
The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. - Can this method be used for other decimals?
Yes, this method applies to any terminating decimal. - What if the decimal is repeating?
Converting repeating decimals involves a different process, often requiring algebraic techniques. - Why is simplifying fractions important?
Simplifying fractions provides the most reduced form, making them easier to understand and work with.
By following these steps, you can confidently convert 0.8125 into its simplest fractional form, enhancing your understanding of the relationship between decimals and fractions. Whether you’re working with measurements, performing calculations, or simply converting decimals, recognizing 0.8125 as a fraction helps provide clarity and precision in your work.
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