The decimal expansion of (72)/(125) will terminate after 2 decimal places. TRUE FALSE

To determine whether the decimal expansion of \(\frac{72}{125}\) will terminate after 2 decimal places, we need to analyze the denominator.<br /><br />The fraction \(\frac{72}{125}\) has a denominator of 125. To check if the decimal expansion terminates, we need to see if 125 is a power of 10 minus 1. Specifically, we need to see if 125 can be written in the form \(2^m \times 5^n\) where \(m\) and \(n\) are non-negative integers.<br /><br />Let's factorize 125:<br />\[ 125 = 5^3 \]<br /><br />Since 125 is a power of 5, it means that the decimal expansion of \(\frac{72}{125}\) will terminate. The number of decimal places it will terminate at is determined by the number of factors of 10 in the denominator. Since 125 has only one factor of 5, the decimal expansion will terminate after 1 decimal place.<br /><br />Therefore, the statement that the decimal expansion of \(\frac{72}{125}\) will terminate after 2 decimal places is FALSE.<br /><br />The answer is: FALSE