What is place value?, Mathematics

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WHAT IS PLACE VALUE? : (This section is only for your assumptions, and not-meant to be passed on to your learners.)

You may have realised that in the decimal system the numerals are represented briefly only 10 symbols, which we call digits. The brevity is achieved because of the simple device used as a basis for the symbolic representation, namely, that it depends completely on the place (or position) in which each digit is written in relation to other digits. For example, ten, hundred and thousand are represented by the same digits, but placed in different positions.

This is possible because we assign different values to different places. These values are the place values (or position values). For example, in the decimal system the values associated with the columns going from right to left, are 1 (i.e.; 10'9, I0 (i.e., lo'), I00 (i.e., lo2), and so on. Therefore, the place value of 4 in 1420 would be 4 x 100, i.e., 400.

Can you guess what the place value of 4 in 1420 is, if we are working in the numeral system whose base is 7 and its powers? In this case the values of the places, going from right to left, are I, 7', 72, 7', ......., i.e., I, 7, 49, 343, and so on. So the place value of 4 would be 4x7?, i.e., 196 (in the decimal system!).

And, how would we represent ten in the binary system, that is, the numeral system whose base is 2 and its powers? In this system instead of ones, tens, hundreds, etc., we would have ones, twos, fours, eights, and so on. Since 10 = (8x I) + 2 = (81) + (4x'O) + (2X I ) + (1 X 0): its representation would be 1010.

The binary system has gained in importance because it is used in computers.

The quandary system (base 5) is used in the Chinese abacus. The duodecimal system (base 12) is used to count things in dozens. The Hexa desimal system (base 60) is used to express time or angles.

You may be able to appreciate the utility of 'place value' when you consider other systems of numerals, like the Roman system. The symbolic representation in this is from left-to right, starting with the symbol representing the largest number. As the numbers get larger and larger, their representation becomes more and more cumbersome. For example, the Roman numeral for the number the numerals formed by using the base 10 system (the decimal system) are called Hindu-Arabic numerals.


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