Final Answer:
The ASTM grain size 7 translates to roughly 1.28*10⁸ grains per square inch without magnification.(Option C)
Step-by-step explanation:
The ASTM grain size number represents the average number of grains per square inch at a magnification of 100x. For a grain size of 7, at 100x magnification, there are approximately 1.28*10⁸ grains per square inch. This value is derived from the relationship between the ASTM grain size number and the actual number of grains per square inch, as calculated by the formula: number of grains per square inch = 2^(n-1), where 'n' is the ASTM grain size number.
When the ASTM grain size is 7, applying the formula gives us 2^(7-1) = 2^6 = 64 grains per linear inch in two dimensions (since the ASTM grain size represents a two-dimensional count). To find the total number of grains per square inch, this count needs to be squared, resulting in 64 * 64 = 4096 grains per square inch.
However, this count is at 100x magnification. To convert this to the original scale without magnification, we need to multiply by the square of the magnification factor, which is 100 * 100 = 10,000. Therefore, 4096 * 10,000 = 1.28*10⁸ grains per square inch without magnification.
Hence, the accurate approximation of grains per square inch without any magnification for an ASTM grain size of 7 is 1.28*10⁸, aligning with option C.