First, we need to identify the hundred position.
The hundred position is the position three places to the left of the decimal point:
#color(red)(6)64#
To round you look to the position to the right of the position you are trying to round to. In this case the #6# to the right of the #6# in the tens place:
#color(red)(6)color(blue)(6)4#
If the digit to the right is less than #5# you keep the digit you are rounding to the same and eliminate all the digits to the right, making them #0#'s up to the decimal point..
If the digit to the right is greater than or equal to #5# you add 1 to the digit you are rounding to and eliminate all the digits to the right,making them #0#'s up to the decimal point..
In this problem the digit to the right is #color(blue)(6)# which is greater than #5#. Therefore, we add #1# to the #color(red)(6)# and eliminate all the digits to the right. making them #0#'s up to the decimal point..
#color(red)(6)color(blue)(6)4# rounded to the nearest hundred is: #color(red)(7)00#
