Final answer:
Estimation is necessary for determining the number of triangles for a string because exact measurements are not always known or practical. Estimation skills, important in mathematics and physics, allow for informed approximations based on qualitative reasoning and previous experience. Approximating to a reasonable precision helps manage impractically large numbers and guide scientific understanding.
Step-by-step explanation:
The reason you have to use estimation to find the number of triangles you need for the string is that the exact number of triangles needed is usually not known in advance. Estimation is a valuable skill in mathematics and physics because it allows us to get a close approximation of a quantity when precise measurements are not possible or practical. Physicists, scientists, and engineers frequently use estimations and guesstimates to approximate quantities based on limited precision of input variables.
For example, when designing a craft such as a string of triangles, you might not know the exact length of each triangle or the exact space they will occupy on the string. By using estimation, you can make an educated guess that will help you approximate these measurements and determine an approximate number of triangles needed. Familiarity with units, understanding of physical principles, and prior experience all aid in making effective estimations.
Additionally, some numbers are impractical to use with their full precision due to their infinite decimal places or the inconvenience of writing many decimal places. This underscores the importance of estimating to a reasonable number of decimal places for practical purposes. These approximations are not random guesses but informed predictions that rely on quantitative reasoning. They also serve as sanity checks to ensure the outcome is within the realm of possibility, helping to guide our understanding of the scientific world.