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:
- Write the decimal as fractions: 0.8125 = 8/10 + 1/100 + 2/100.
- 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.
- Divide both the numerator and denominator by 125 to simplify the fraction: (8125÷125)/ (10000÷125) = 65/80.
- 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.