Fractions represent parts of a whole or a quantity that has been divided into equal parts. Decimals, on the other hand, represent the same idea of parts of a whole but use a base-ten place value system.

Answer: 0.8125 as a fraction is 13/16​.

To convert the decimal 0.8125 into a fraction, we can utilize its place value. In 0.8125, the digit 8 is in the tenth-place, 1 is in the hundredth-place, and 2 is in the thousandth-place. This means that 0.8125 can be expressed as 810108​ for the tenths, 11001001​ for the hundredths, and 2100010002​ for the thousandths. We can then add these fractions together:

1. Write the decimal as fractions: 0.8125 = 8/10 + 1/100 + 2/100​.
2. Simplify the fraction by finding the greatest common divisor (HCF) of the numerator and denominator. In this case, the HCF of 8125 and 10000 is 125.
3. Divide both the numerator and denominator by 125 to simplify the fraction: (8125÷125)/ (10000÷125) = 65/80​.
4. Further simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5 in this case: (65÷5)/ (80÷5) = 13/16​.

So, 0.8125 as a fraction, when simplified to its lowest terms, is 13/16​.

This conversion is a fundamental mathematical skill, allowing for precise representation of decimal values, especially in scientific, engineering, and financial contexts, where accuracy and fractions are essential.