## Materials Science and Engineering: An Introduction

$n =4.81 \approx 4.8$
Given: 25 grains per square inch at a magnification of 75x. Required: ASTM grain-size number Solution: Using Equation 4.18, we find: $N_{M}(\frac{M}{100})^{2} = 2^{n-1}$ $N_{M}$ = 25 = number of grains at magnification M (75) $(25)(\frac{75}{100})^{2} = 2^{n-1}$, Solving for $n$, we find: $n = \frac{log N_{m} + 2 log \frac{M}{100}}{log 2} + 1 = \frac{log 25 + 2 log \frac{75}{100}}{log 2} +1 =4.81$