**Place-value**is the system we use to represent numbers. Place-value systems are much more advanced and useful than other number systems such as Roman or Egyptian systems. (For example, would you prefer to work out 72 x 39 using your knowledge of our number system or LXXII x XXXIX using only a knowledge of Roman numerals?) Place-value, together with the concept of zero, are of significant importance in the development of arithmetic and mathematics. The place-value system we use in everyday life is

**base-10**, with increasing columns for ones (or units), tens, hundreds, thousands etc. To deal with parts of wholes, there are decreasing place value columns after the decimal point, starting with tenths, hundredths, thousandths and so on. The main advantage of our place value system is that any number can be represented using just 10 symbols – 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These are the Arabic numerals, which originated from the similar Hindu symbols. Another advantage is that it is easy to see at a glance the rough size of a number by looking at its number of digits. In Roman numerals, it is not obvious that LXXII is in fact greater than XXXIX. Base-10 is just one possible place-value system. We probably use base-10 because we have ten fingers, but it is possible to use any other base. In base-9, for example, we would have columns for ones (or units), nines, eighty-ones etc. Only the digits 0-8 would be used, and the number nine itself would be written as ’10’ since in base-9 this represents ‘one nine and zero units’.

**Base-2**(or

**binary**), which uses only 0s and 1s, is of huge importance in computing. In base-10, each column increases by a factor of 10, but in base-2, we have ones (or units), twos, fours, eights, sixteens and so on. So the binary number 10111 would represents 1 sixteen, 0 eights, 1 four, 1 two and 1 unit, which would be 23 in base-10. Base-8 and base-16 are also commonly used in computing.