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The Impact of Place Value on Mathematics (page 2)

By — Pearson Allyn Bacon Prentice Hall
Updated on May 5, 2014

The Hindu-Arabic Numeration System:

The Hindu-Arabic place value numeration system is based on the principle of collection and exchange of groups of 10. In this system, 10 ones can be traded and represented by one group of 10, 10 groups of 10 each can be exchanged and represented as 100, 10 groups of 100 each can be regrouped and represented as 1,000, and so on. This mechanism of collection and exchange makes possible a system in which only 10 unique symbols are necessary to express any quantity.

The total value of a number is determined by multiplying each quantity by the value of its position or place and then adding all those values together. The following example indicates how the total value is found for 47 and for 385.

(4 X10) + (7 X 1) =  47

(3  x 100) + (8 X 10) + (5 X 1) = 385

Several important properties of the base-10 place value system include:

1. Ten unique symbols (0–9) express any numerical quantity.

2. The value of each base-10 place is multiplied by 10 as the digits move to the left from the ones place.

 

Quantity: 4 3 2
Place Value: 100 10 1
Total Value: 400 30 2

3. The decimal point is a symbol that enables the system to express parts of numbers. As one moves to the right of the decimal point in a number, the value of each place is divided by 10 (tenths, hundredths, thousandths, and so on). For example, the value of each place is as follows:

0.       2          3          4             5

         .1        .01     .001     .0001

4. The zero symbol (0) is a placeholder that represents a set that has no members or elements and is integral to expressing and computing quantity.

 

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