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Simplifying a fraction means making it as simple as possible. This process involves reducing both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). This is a crucial step because it makes the fraction easier to work with and understand. In the case of converting decimal 0.085 to a fraction, we initially get \(\frac{85}{1000}\). Although this fraction represents the correct value, it can be simplified further. We divide both 85 and 1000 by 5 (their GCD) to get the simplest form, \(\frac{17}{200}\). Simplifying fractions helps in comparing and using them in different mathematical operations. Always look for the GCD before simplifying to ensure you get the fraction in its lowest terms.

The greatest common divisor (GCD) of two numbers is the largest number that divides both of them evenly. To simplify a fraction, finding the GCD is a necessary step. Let's look at our example of converting 0.085 to a fraction. We first get the fraction \(\frac{85}{1000}\). To simplify it, we need to find the GCD of 85 and 1000.

One way to find the GCD is through the factorization method. List the prime factors of each number:
* For 85: 5, 17
* For 1000: 2, 2, 2, 5, 5, 5
Next, we identify the common factor(s), which is 5 in this case. Therefore, the GCD is 5. By dividing both the numerator and the denominator by their GCD (5), we can simplify the fraction to \(\frac{17}{200}\). Utilizing the GCD not only helps simplify fractions but also is essential in various mathematical problem-solving contexts.

Decimals are often converted to fractions using powers of 10. This is because each place value in a decimal number represents a power of 10. For instance, the number 0.085 has three decimal places. Each place value (tenths, hundredths, thousandths) corresponds to a power of 10:
* 0.1 is \(\frac{1}{10}\)
* 0.01 is \(\frac{1}{100}\)
* 0.001 is \(\frac{1}{1000}\)
So, 0.085 can be written as \(\frac{85}{1000}\). This is because the number 85 is in the thousandths place. Power of 10 is crucial in converting decimals to fractions accurately. Understanding this concept makes it much easier to work with decimals and fractions, as it allows you to seamlessly convert between the two forms.