Final answer:
Studying fixed-point number manipulation is vital for efficient real-world calculations and helps develop practical mental math skills. Significant figures ensure accuracy in operations like addition and subtraction, and managing approximations is essential in scientific and numerical work. Additionally, working with estimates is often more practical than using exact, often infinite, numbers.
Step-by-step explanation:
Studying fixed-point number manipulation is important because it allows us to make more efficient and practical calculations in everyday life. By using approximations, we can perform mental math more easily and develop a lifelong skill that becomes second nature. It is also essential to understand that numbers in the real world are often approximations rather than exact values, and learning how to estimate can reduce the stress that comes with onerous systems like significant digits.
Significant figures are crucial in fundamental computations such as addition and subtraction, where the result should only contain as many decimal places as the least certain number used in the calculation. This emphasizes the efficient and accurate representation of data, which is vital in scientific, engineering, and technical fields.
In the context of shapes and volumes, a solid grasp of fixed-point number manipulation helps to streamline complicated formulas and allows us to understand measurements and their corresponding units. Remember that units must be consistently carried through all mathematical operations.
Lastly, certain numbers can be infinitely long, making it impractical to use them in their entire length. Estimating to a specific number of decimal places is often more convenient and does not significantly impair precision, which is why we must be judicious about the number of digits we use in our calculations.