I've had friends audited for not declaring cents of interest they earned when their landlords placed security deposits in savings accounts...
The first is to put whole dollar amounts on all the lines on all the forms, and to round those as you say. Even that one doesn't round all intermediate numbers used in calculations, only the lines on the form.
The other is to be precise to the penny.
Both are allowed by the official instructions, even if software like TurboTax Online always picks the first.
However, if you do things by hand there is some ambiguity whenever you have a choice to bundle or unbundle accounts, because if you enter them separately, you've rounded before the sum, but if you enter one total, you are supposed to round after the sum. You can save a buck here and there if you want.
One example of how preliminary numbers (a better phrase than intermediate) aren't rounded would be if someone has three Forms W-2 in a year, such as from three jobs. All three Box 1 amounts are added up unrounded regardless of whether you put a whole dollar wage total on Form 1040. If the three Box 1 amounts end in 35 cents, 40 cents, and 45 cents (just to pick a suitable example), you're going to show an extra buck of wage income than if you could round those cents away.
IRS guidance from the 1040 instructions:
"You can round off cents to whole dollars on your return and schedules. If you do round to whole dollars, you must round all amounts. To round, drop amounts under 50 cents and increase amounts from 50 to 99 cents to the next dollar. For example, $1.39 becomes $1 and $2.50 becomes $3.
If you have to add two or more amounts to figure the amount to enter on a line, include cents when adding the amounts and round off only the total."
I that because the landlord filed a form but the tenant didn't file a form to match?