Mathematics Principles V11

Clive W. Humphris

NUMBER SYSTEMS: Addition.  


To avoid errors when adding a column of numbers a tidy approach is required. This is especially important because each number has what is called a place value. Those columns to the left of the units progressively increase by a factor of ten as you move to the left, i.e. units, tens, hundreds etc. The maximum number that any group of digits can represent is always one less than the heading of the column to its left. Say 99 when the column heading on the left of that number is hundreds or 999,999 when the left column represents millions.

A value of 1 in the tens column means ten, as 5 means 5 tens, and 3 in the ten-thousands column represents thirty thousand. As each position to the left is a multiplier of ten it is important that when adding you list all the units then all the tens and then hundreds together etc, and so on.

Inserting additional zeros to the right of a number multiplies that number by 10 for each one, i.e. 230 is two-hundred and thirty, 2300 is two-thousand-three-hundred. Zeros placed at the high end of a number have no place value and can be ignored or removed.

As each column is totalled, those coming to more than 9 will produce a carry. This is then written down under the column to the left and forms part of the addition in that column. For example, say in the tens and units' columns you have 29, 26 and 28 then 9 + 6 + 8 = 23. Three units and two tens. The tens must be carried over and added in the correct column to the left.


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