Decimals

Decimals - more accurately the Decimal Number System - was an amazing invention, for several reasons.

• It is a positional number system, meaning that the location of a digit in a number influences its value.
  • For example, in the numbers $30$ and $300$, the $3$ represents different values. In the first, it is $3 \times 10^1$ and in the second it is $3 \times 10^2$
  • Before the invention of positional number systems, you had to keep adding characters to represent larger numbers. For example, this is the number $3$,$888$ in Roman numerals:
    • MMMDCCCLXXXVIII
• It uses only $10$ characters to express an infinite number of numbers:
  • $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$
• It is a "base-10" number system. This is intuitive to humans, likely because we have ten fingers.
  • There are other "base" systems, like binary ($2$ characters), hexadecimal ($16$ characters), vigesimal ($20$ characters), and sexagesimal ($60$ characters).
  • It's true that other "base" systems have fewer characters, but they wouldn't be as intuitive (remember our $10$ fingers).
• It uses the digit $0$ to indicate "there is nothing in this place." This is an incredibly useful invention.
  • For example, in the number $405.02$, the $0$s tell us there is nothing in the tens place or tenths place.

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If you're from Europe or Latin America

Chances are that you reverse the comma and the dot. For example, instead of 3,456.78 such students will write 3.456,78 (in a few cases, the thousands separator is replaced by a space, so 3 456,78). 

You cannot do this on the GRE, irrespective of where you take the test. Don't worry too much though - the GRE ignores commas entirely (i.e, you cannot use a thousands separator) so you should be able to find out if you've made a mistake.