To round one and three-quarters (1.75) to the nearest whole number, we follow these rules:

1. If the decimal part is less than 0.5, round down to the nearest whole number.
2. If the decimal part is 0.5 or greater, round up to the nearest whole number.

In this case, the decimal part (0.75) is greater than 0.5, so we round up to the nearest whole number, which is 2.

So, one and three-quarters (1.75) rounded to the nearest whole number is 2.