06.23.2018: One Chapter of Math

Today's soundtrack is Kevin Max: Serve Somebody, which features a beautiful reprise of the dcTalk song "Red Letters."

This morning, I'm working on the first chapter of part 5, "The Part of Tens," in Basic Math & Pre-Algebra For Dummies Workbook, "Ten Alternate Numeral and Number Systems."

The chapter opens with a definition that differentiates numbers and numerals: "A number is an idea that expresses how much or how many. A numeral is a written symbol that expresses a number" (p. 279). This chapter will look at different ways from expressing numbers and numerals from the one we are accustomed to, the "Hindu-Arabic (decimal) system" (p. 279).

Humans started representing numbers by showing an actual quantity of the physical thing itself. Then they moved on to using tally marks. After that, they moved on to bundled tally marks.

The numeral system created by the Egyptians "are among the oldest number systems still in use today" (p. 280). They were the first to use discrete symbols to represent multiples of numbers. Interestingly, their "symbol for 1,000,000 also stands for infinity" (p. 280).

In approximately 4,000 BC, the Babylonians created a numeral system based on the numbers 6 and 60. They used separate symbols to represent ones and tens, and differentiated the way that numbers were represented depending on whether the number was under 60 or 60+. The Babylonians "had no symbol for zero to serve as a placeholder," which can cause some confusion, as "the symbol for 60 is the same as the symbol for 1" (p. 281).

The ancient Greeks created a number system very similar to ours, but instead of adding 0s to the end of their numbers to show multiples of ten, they had separate symbols for 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, and 900.

In 2,000 BC, the Romans developed their numeral system, which is still in use to an extent today. The Roman system uses seven symbols: "I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000" (p. 282). The fourth installment in the Grand Theft Auto series was stylized as Grand Theft Auto IV (4).

At the same time that the Babylonians were developing their numeral system, the Mayans in South America were also creating a numeral system, using dots and bars and placements to indicate their values. Their "place value is based on the number 20" (p. 283).

Computers use the "Base-2 (Binary) Numbers" (p. 283) system. The binary system is based "on powers of two (2⁰, 2¹, 2², 2³, [...] and so on" (p. 283).

Computer programmers use the "Base-16 (Hexadecimal) Numbers" system so that they can easily read the numbers that they are going to use and then convert them to the binary system.

Prime-based numbers "use place value to determine the value of digits" (p. 285), and are based on multiplication instead of addition.