Suppose you estimate the Simple Linear Regression Model via OLS:
$$y_i = \beta_0 + \beta_1 x_i + u_i,$$
...obtaining estimates of 2.1 for the constant and 4.76 for the slope term. The constant term is statistically significant at the five percent significance level, but the slope term is not -- falling just short of significance (i.e. it has a p-value of 0.064, slightly above the significance benchmark of 0.05).
Your classmate suggests that you should change the units of the $x_i$ variable to make the estimate of $\beta_1$ larger and, therefore, statistically significant.
Does your classmate's idea make sense?