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0.378 to the nearest hundreds place is zero.
That is rounded to the hundreds place. The 7 is in the tenths place and the 5 is in the hundreds place. If you want to round it to the tenths place though, it would be 0.8 because 5's always round up.
You cannot round a number with a place value larger than the place value you seek to round it to. i.e. You cannot round thousands to hundreds, hundreds to tens, tens to ones, etc.
7.868 to the nearest hundreds place is zero. To the nearest hundredths place is 7.87
To round to the hundreds place, look at the tens place. Since it is greater than or equal to 5, you should round up. It is 900.