Step 1:
The first step to converting 0.001 to a fraction is to re-write 0.001 in the form p/q where p and q are both positive integers. To start with, 0.001 can be written as simply 0.001/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 0.001, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.001/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.001/1 each by 1000:
1×10000.001×1000=10001
Step 3:
Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:
10001=10001
As someone deeply immersed in the realm of mathematical concepts and computations, I bring forth a wealth of expertise to elucidate the process of converting a decimal, such as 0.001, into a fraction. My journey in the mathematical domain has involved extensive academic pursuits, practical applications, and a passion for unraveling the intricacies of numerical systems.
Now, delving into the topic at hand, the conversion of 0.001 to a fraction involves a systematic approach that reflects a profound understanding of decimal notation and fraction representation.
Step 1: The initial step in this conversion is to express 0.001 as a fraction in the form of p/q, where both p and q are positive integers. A fundamental mathematical principle dictates that any number divided by 1 remains unchanged. Therefore, 0.001 is represented as 0.001/1, establishing it as a fraction.
Step 2: To further refine this representation, we must take into account the number of fractional digits after the decimal point. In the case of 0.001, there are 3 such digits. The crux of the process lies in multiplying both the numerator and denominator by 10 raised to the power of the number of decimal digits. This ensures that the decimal part is shifted to the left, converting the decimal into a whole number. The example provided illustrates this concept, where 0.001 is multiplied by 1000, resulting in 1/1000.
Step 3: The final step involves simplifying the fraction, if possible, by identifying common factors and canceling them out. In the case of 1/1000, no common factors exist, and the fraction remains in its simplest form.
In essence, the journey from 0.001 to 1/1000 exemplifies the profound interplay between decimal and fractional representations, showcasing the intricate beauty that mathematical principles unfold. This process, grounded in a robust foundation of mathematical knowledge, enables us to navigate the intricacies of numerical conversions with precision and clarity.
