To round any number, look at the digit to the right of the place you are rounding to. If the digit is 5 or more, change the digit in the place you are rounding to to the next higher digit. If the digit to the right of the place you are rounding to is less than 5, leave the digit in the place you are rounding to as it is. Change all digits to the right of the place you rounded to to zeros.
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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.