Positional weighting of a number

Answer 1

positional weighting is the system we use in Base 10 to allow us to express any possible number in any possible magnitude. It works by assigning certain positions what are called powers and then multiplying any unit placed in that position by the corresponding power.

In Base 10 we use positional weighting to allow Units, Tens and Thousands as just one example shown below is how this works:

We only have 10 units available to us in the Base 10 system

0,1,2,3,4,5,6,7,8,9

but using the positional weighting system we can alter the value of a unit depending on what position it is placed in.

Assume that the units column the first column to the left of the decimal point has a positional weighting of 10*0 so any unit placed in that column is multiplied by 10*0 which (because multiplying 10 by 0 results in 0) is the same as performing no multiplication on the unit leaving it a 9.

The next column has the weighting 10*1 which is the same as multiplying by 10 so each unit in the column to the left of the units column is worth a multiple 10 of the displayed unit eg 9 x 10*1 (ten to the power of 1 = 10). This is where the 'Tens' column gets its name from.

The column to the left of the tens column has a weighting of 10*2 (ten squared = 100) meaning that each unit in that column is worth 100 times the value shown, eg 9 x 10*2 = 900. This is where the 'Hundreds' column gets its name from.

9 x 10*0 = 9
9 x 10*1 = 90
9 x 10*2= 900

I hope this helps, one important thing to remember is that the weighting will change depending on what Base you are working in. If you were working in Base 2 for example instead of 10*0, 10*1, 10*2 etc you would see 2*0, 2*1, 2*3 etc.