I would be very cautious about labeling a coefficient "small" unless all of the measurements have been normalized. In the following example, I look at the correlation between the Mass of some objects and their length. As the units of the length change, the absolute size of the fit coefficient changes but the p value is constant and any practical significance would also be constant.

```
set.seed(1)
DF <- data.frame(Meters = c(1.5, 1.6, 1.7, 1.8),
Mass = c(1.5, 1.6, 1.7, 1.8) * 1.5 + rnorm(4, mean = 0 , sd = 0.1),
KM = c(1.5, 1.6, 1.7, 1.8)/1000,
MM = c(1.5, 1.6, 1.7, 1.8) * 1000)
summary(lm(Mass ~ Meters, data = DF))
#>
#> Call:
#> lm(formula = Mass ~ Meters, data = DF)
#>
#> Residuals:
#> 1 2 3 4
#> 0.01412 0.03867 -0.11971 0.06692
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.9237 0.7489 -1.233 0.3427
#> Meters 2.0646 0.4528 4.559 0.0449 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.1013 on 2 degrees of freedom
#> Multiple R-squared: 0.9122, Adjusted R-squared: 0.8684
#> F-statistic: 20.79 on 1 and 2 DF, p-value: 0.04489
summary(lm(Mass ~ KM, data = DF))
#>
#> Call:
#> lm(formula = Mass ~ KM, data = DF)
#>
#> Residuals:
#> 1 2 3 4
#> 0.01412 0.03867 -0.11971 0.06692
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.9237 0.7489 -1.233 0.3427
#> KM 2064.5932 452.8179 4.559 0.0449 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.1013 on 2 degrees of freedom
#> Multiple R-squared: 0.9122, Adjusted R-squared: 0.8684
#> F-statistic: 20.79 on 1 and 2 DF, p-value: 0.04489
summary(lm(Mass ~ MM, data = DF))
#>
#> Call:
#> lm(formula = Mass ~ MM, data = DF)
#>
#> Residuals:
#> 1 2 3 4
#> 0.01412 0.03867 -0.11971 0.06692
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.9236577 0.7488628 -1.233 0.3427
#> MM 0.0020646 0.0004528 4.559 0.0449 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.1013 on 2 degrees of freedom
#> Multiple R-squared: 0.9122, Adjusted R-squared: 0.8684
#> F-statistic: 20.79 on 1 and 2 DF, p-value: 0.04489
```

^{Created on 2021-03-25 by the reprex package (v0.3.0)}