Study Guide: Decimal System
The Decimal Number System, also called Hindu-Arabic number system, is a positional numeral system that uses 10 as the base and requires 10 different symbols which are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It also uses a dot (the decimal point) to represent fractions. In this system, the numerals used to show a value take different place values depending upon position. In a base-10 system the number 543.21 represents the sum:
$$(5 \times 10^2) + (4 \times 10^1) + (3 \times 10^0) + (2 \times 10^{−1}) + (1 \times 10^{−2})$$
History
- Invented in India.
- Brought to Persia and Arabian around the 8th century CE.
- Brought to Europe in the 12th century CE.
- Brought to the Americas in the 15th century CE.
- Spread worldwide by the European and American empires.
The advantages the positional system are so numerous that the Hindu-Arabic numerals, and the base-10 system have been adopted almost everywhere. This might be the closest humanity has to a universal language.
Place Value
The place (or position) of a symbol determines its value (the actual numeric quantity).
In the below examples, the only thing that changes is the position of the symbol $1$, but the value of that symbol changes by multiples of $10$ from very large to very small.
\begin{array}{lrll} \hline Name & Value & Prefix & Symbol \\\ \hline trillion &1,000,000,000,000 & tera & T \\\ billion &1,000,000,000 & giga & G \\\ million &1,000,000 & mega & M \\\ thousand &1,000 & kilo & k \\\ hundred &100 & hecto & h \\\ ten &10 & deka & da \\\ unit &1 & & \\\ tenth &0.1 & deci & d \\\ hundredth &0.01 & centi & c \\\ thousandth &0.001 & milli & m \\\ millionth &0.000,001 & micro & µ \\\ billionth &0.000,000,001 & nano & n \\\ trillionth &0.000,000,000,001 & pico & p \\\ \hline \end{array}