Title 2 Mathematics in everyday life

2.1 Numeral system 2.2 Gradient 2.3 Isobaric lines 2.4 Contour lines

2.1 A numeral is a writing system for expressing numbers, that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

2.1.1 Decimal number system

The decimal numeral system (also called base ten or occasionally denary) has ten as its.

Positional decimal systems include a zero and use symbols (called digits) for the ten values (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent any number.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ต ำแหน่งของเลขโดดในฐำนสิบใช้แสดงค่ำของตัวเลขนั้นที่ต ำแหน่งของเลขฐำนยกก ำลังของต ำแหน่ง

Example 623 = 600 + 20 + 3 = (6 x 100) + (2 x 10) + (3 x 1) = (6 x 102) + (2 x 101) + (3 x 100) Notation Position (i) 3 2 1 0 . -1 -2 -3

Value (Ri) 103 102 101 100 . 10-1 10-2 10-3

78.25 = (7 x 101) + (8 x 100) + (2 x 10-1) + (5 x 10-2)

= 70 + 8 + 0.2 + 0.05

Binary number system Binary numeral system, represent numeric values using 2 symbols : 0 and 1

Example (1101)2

= (1 x 23) + (1 x 22) + (0 x 21) + (1 x 20) = 8 + 4 + 0 + 1 = 13

Notation position (i) 3 2 1 0 . -1 -2 -3 value(Ri) 23 22 21 20 . 2-1 2-2 2-3

Example (101.11)2 (1 x 22) + (0 x 21) + (1 x 20) + (1 x 2-1) + (1 x 2-2) = 4 + 0 + 1 + 0.5 + 0.25 = 5.75

The decimal (base ten) numeral system has ten possible values (0,1,2,3,4,5,6,7,8, and 9) for each place-value. In contrast, the binary (base two) numeral system has two possible values, often represented as 0 or 1, for each place-value.

How to covert from Decimal to Binary

The decimal (base ten) numeral system has ten possible values (0,1,2,3,4,5,6,7,8, and 9) for each place-value. In contrast, the binary (base two) numeral system has two possible values, often represented as 0 or 1, for each place-value.

How to covert from Decimal to Binary

Answer (29)10

= (11101)2

14 0

1

7

3 2

1

1

1

2 29

2

2

2 1

Answer (0.65625)10

= (0.10101)2

(0.65625)10

Binary ???

2 x 0.65625 = 1.3125 1

2 x 0.3125 = 0.625 0

2 x 0.625 = 1.250 1

2 x 0. 25 = 0.50 0

2 x 0. 5 = 1.00 1

(27.125)10 binary

2 27 = 13 1 0.125 2 13 = 6 1 2 2 6 = 3 0 0 .250 2 3 = 1 1 2 2 1 1 0 .500 2 1 .000

Example

Answer = (11011.001)2

X

X

X

Octal number system • The octal numeral system is the base-8 number

system and uses the digits 0 to 7.

Convert to Decimal

(142)8 = (1 x 82) + (4 x 81) + (2 x 80) = 64 + 32 + 2 = 98

Notation Position (i) 3 2 1 0 . -1 -2 -3 Value (Ri) 83 82 81 80 . 8-1 8-2 8-3

512 64 8 1 8

1

64

1

512

1

(13.23)8 = (1 x 81) + (3 x 80) + (2 x 8-1) + (3 x 8-2) = 8 + 3 + 0.25 + 0.046875 = 11.296875

(28.125)10

8 28 = 3 4 0.125

8 3 3 8 1 .000

Decimal to Octal

X

Answer (28.125)10 = (34.1)8

Hexadecimal number system

• Hexadecimal (base-16, or hex) is a positional

numeral system with a radix or base -16.

• It uses sixteen distinct symbols.

• 0, 1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

• A=10, B=11, C=12, D=13, E=14 and F=15

For example(Base-16 to Base-10) (3B)16 = (3 x 161) + (B x 160) = (3 x 16) + (11 x 1) = 48 + 11 = 59 Notation

Position (i) 3 2 1 0 . -1 -2 -3

Value (Ri) 163 162 161

160 16-1 16-2 . 16-3

4096 256 16 1

(BE.3)16 = (Bx161) + (Ex160) + (3x16 -1) = (11x16) + (14x1) + (3x0.0625) = 176 + 14 + 0.1875 = 190.1875

(Base-16 to Base-10)

A=10, B=11, C=12, D=13, E=14 and F=15

For Example: (27.125)10

Answer (27.125)10 = (1B.2)16

(Base-10 to Base-16)

16 27 =1 11 = B

16 1 1

0.125 x

16 2 .00

Convert your student id no. to Binary, Octal and Hexadecimal numeral system and save (the solution method) in PDF format.

Conditions: 1- 7 position are integer and 8 - 10 are decimal.

Email: rsermsak@hotmail.com

Homework

For example in Binary, Student ID: 5604530497

5604530.497 5604530 0.497

2 5604530 = 2802265 0

2 2802265 = 1401132 1

2 1401132 = 700566 0

2 700566 = 350283 0

2 350283 = 175141 1

2 175141 = 87570 1

2 87570 = 43785 0

2 43785 = 21892 1

2 21892 = 10946 0

2 10946 = 5473 0

2 5473 = 2736 1

2 2736 = 1368 0

2 1368 = 684 0

2 684 = 342 0

2 342 = 171 0

2 171 = 85 1

2 85 = 42 1

2 42 = 21 0

2 21 = 10 1

2 10 = 5 0

2 5 = 2 1

2 2 = 1 0

1

0 0.497 x 2 0.994

1 0.994 x 2 1.988

1 0.988 x 2 1.976

1 0.976 x 2 1.952

1 0.952 x 2 1.904

1 0.904 x 2 1.808

1 0.808 x 2 1.616

1 0.616 x 2 1.232

0 0.232 x 2 0.464

0 0.464 x 2 0.928

1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 . 0 1 1 1 1

Answer