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From Wikipedia

Dot-decimal notation

Dot-decimal notation is a presentation format for numerical data. It consists of a string of decimal numbers, each pair separated by a full stop (dot).

A common use of dot-decimal notation is in information technology where it is a method of writing numbers in octet-grouped base-10 (decimal) numbers separated by dots (full stops). In computer networking, Internet Protocol Version 4 addresses are commonly written using the quad-dotted notation of four decimal integers, ranging from 0 to 255 each.

Definition and use

Dot-decimal notation is a presentation format for numerical data expressed as a string of decimal numbers each separated by a full stop.

For example, the hexadecimal number0xFF0000 is expressed in dot-decimal notation as 255.0.0.

In computer networking, the term is often used as a synonym of dotted quad notation, or quad-dotted notation, a specific use to represent Internet Protocol Version 4 addressess.

Object identifiers use a style of dot-decimal notation to represent an arbitrarily deep hierarchy of objects identified by arbitrary decimal numbers.

Common decimal fractions are sometimes said to be written in dotted decimal notation. For example the fraction 1/8 is represented as 0.125.

An Internet Protocol Version 4 (IPv4) address consists of 32 bits, which may be divided into four octets. These four octets are written in decimal numbers, ranging from 0 to 255, and are concatenated as a character string with full stop delimiters between each number.

For example, the address of the loopback interface, usually assigned the host name localhost, is 127.0.0.1. It consists of the four binary octets 01111111, 00000000, 00000000, and 00000001, forming the full 32-bit address.

Caveat

In information technology, an integer number that starts with the digit 0 is often interpreted as a number in octal representation. Therefore, if an IP address component is written with a leading 0 digit, it may be interpreted incorrectly by some utility programs. For example, the representation 022.101.031.153 is interpreted as 18.101.25.153 in decimal notation.

Positional notation

Positional notation or place-value notation is a method of representing or encoding numbers. Indian mathematicians developed the Hindu-Arabic numeral system, the modern decimal positional notation in the 9th century. Positional notation is distinguished from other notations (such as Roman numerals) for its use of the same symbol for the different orders of magnitude (for example, the "ones place", "tens place", "hundreds place"). This greatly simplified arithmetic and led to the quick spread of the notation across the world.

With the use of a radix point, the notation can be extended to include fractions and the numeric expansions of real numbers.

History

Today, the base 10 (decimal) system is ubiquitous. It was likely motivated by counting with the ten fingers. However, other bases have been used. For example, the Babylonian numeral system, credited as the first positional number system, was base 60.

Counting rods and most abacuses in history represented numbers in a positional numeral system. Before positional notation became standard, simple additive systems (sign-value notation) were used such as Roman Numerals, and accountants in ancient Rome and during the Middle Ages used the abacus or stone counters to do arithmetic.

With counting rods or abacus to perform arithmetic operations, the writing of the starting, intermediate and final values of a calculation could easily be done with a simple additive system in each position or column. This approach required no memorization of tables (as does positional notation) and could produce practical results quickly. For four centuries (13th&ndash;16th) there was strong disagreement between those who believed in adopting the positional system in writing numbers and those who wanted to stay with the additive-system-plus-abacus. Although electronic calculators have largely replaced the abacus, the latter continues to be used in Japan and other Asian countries.

Georges Ifrah concludes in his Universal History of Numbers:

Thus it would seem highly probable under the circumstances that the discovery of zero and the place-value system were inventions unique to the Indian civilization. As the Brahmi notation of the first nine whole numbers (incontestably the graphical origin of our present-day numerals and of all the decimal numeral systems in use in India, Southeast and Central Asia and the Near East) was autochthonous and free of any outside influence, there can be no doubt that our decimal place-value system was born in India and was the product of Indian civilization alone.|

Aryabhata stated "sthÄ�nam sthÄ�nam daÅ›a guá¹‡am" meaning "From place to place, ten times in value". His system lacked zero. The zero was added by Brahmagupta. Indian mathematicians and astronomers also developed Sanskrit positional number words to describe astronomical facts or algorithms using poetic sutras.

A key argument against the positional system was its susceptibility to easy fraud by simply putting a number at the beginning or end of a quantity, thereby changing (e.g.) 100 into 5100, or 100 into 1000. Modern cheques require a natural language spelling of an amount, as well as the decimal amount itself, to prevent such fraud.

Mathematics

Base of the numeral system

In mathematical numeral systems, the base or radix is usually the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is 10, because it uses the 10 digits from 0 through 9.

The highest symbol of a positional numeral system usually has the value one less than the value of the base of that numeral system. The standard positional numeral systems differ from one another only in the base they use.

The base is an integer that is greater than 1 (or less than negative 1), since a radix of zero would not have any digits, and a radix of 1 would only have the zero digit. Negative bases are rarely used. In a system with a negative radix, numbers may have many different possible representations.

(In certain non-standard positional numeral systems, including bijective numeration, the definition of the base or the allowed digits deviates from the above.)

In base-10 (decimal) positional notation, there are 10 decimal digits and the number

2506 = 2 \times 10^3 + 5 \times 10^2 + 0 \times 10^1 + 6 \times 10^0 .

In base-16 (hexadecimal), there are 16 hexadecimal digits (0â€“9 and Aâ€“F) and the number

171\mathrm{B} = 1 \times 16^3 + 7 \times 16^2 + 1 \times 16^1 + \mathrm{B} \times 16^0 (where B represents the number eleven as a single symbol)

In general, in base-b, there are b digits and the number

a_3 a_2 a_1 a_0 = a_3 \times b^3 + a_2 \times b^2 + a_1 \times b^1 + a_0 \times b^0 (Note that a_3 a_2 a_1 a_0 represents a sequence of digits, not implicit multiplication)

Digits and numerals

In order to discuss bases other than the decimal system (base ten), a distinction needs to be made between a number and the digit representing that number. Each digit may be represented by a unique symbol or by a limited set of symbols.

For example, in the decimal positional numeral system, there are ten possible digits in each position. These are "0", "1", "2", "3", "4", "5", "6", "7", "8" , and "9" (henceforth "0-9"). In other bases, the digits used may be unfamiliar or may be used to indicate numbers other than those they represent in the

Question:I know that if you let x=0.888888 and 10x=8.888888 then is it always divided by 9? I know the answer is 8/9. BONUS! PLEASE ANSWER! What do you do if you have to convert 4.4 barred into a fraction?

Answers:It depends on how many digits repeat. If you had 4.4 barred, you'd do the .4 barred which will come out 4/9 then make it a mixed number, 4 4/9. 8.7 barred 7 would be 8 7/9. Sometimes you'll end up with a number other than 9 or 99 at the end but you always use 9, 99, 999, etc to start. Like for 0.1363636 (barred 63) Two digits repeat so multiply by 100 (two zeros) 100x = 13.636363 - x = 0.136363 ----------------------------- 99x = 13.500000 so x = 13.5/99 but you can't have a decimal in a fraction so multiply top and bottom by 10 135/990 (then reduce)

Question:what are these numbers scientific notation 56,000 70,000 20,000 Now, assume each number for task 1 doubles. Show how each number is multiplied by 2 and find the new numbers. Be sure each number is in scientific notation!

Answers:In scientific notation you write a number with a long string of zeros in a shorthand fashion. 56000 Look at the first non-zero part and rewrite as a number between 1 and 10 56 -> 5.6 Compare where the decimal is now (after the 5) and where it was originally (4 places to the right or positive 4). This tells you the power of 10 to use. 56000 = 5.6x10^4 or 5.6E4 in calculator speak. The others work the same 70000 = 7.0x10^4 = 7.0E4 20000 = 2.0x10^4 = 2.0E4 What happens if you double a number in scientific notation? 2x(5.6x10^4) = 11.2x10^4, but this breaks the rule about the significant part being between 1 and 10. 11.2 = 1.12x10 11.2x10^4 = 1.12x10x10^4 = 1.12x10^5 or 1.12E5 Or 2x56000 = 112000 = 1.12x10^5 (because the decimal should be 5 to the right from its new location) 2x70000 = 140000 = 1.4x10^5 2x20000 = 40000 = 4.0x10^4 (Notice the power of ten doesn't change here.) Just in passing... .00000645 = 6.45x10^-6 = 6.45E-6 because the decimal belongs 6 steps to the left of its new location.

Question:1. Write the following value in scientific notation. 23,000,000 - 2.3 x 106 - 2.3 x 107 - 2.3 x 10-5 - 2.3 x 102 2. Write the following value in scientific notation. 7,400,000 - 7.4 x 106 - 7.4 x 107 - 7.4 x 10-5 - 7.4 x 102 3. Write the following value in scientific notation. 0.00000021 - 2.1 x 106 - 2.1 x 10-6 - 2.1 x 105 - 2.1 x 10-7 4. Write the following value in scientific notation. 0.00003165 - 3.165 x 106 - 3.165 x 10-6 - 3.165 x 10-5 - 3.165 x 108 5. Which value below is not equivalent to the others? - 7.27 x 101 - 72.7 - 727 x 100 - 7.27 x 10 6.Anything raised to the zero power will equal 1. True False 7. Write the following value in standard notation. 4.25 x 106 - 425,000 - 4,250,000 - 425,610 - 425,000,000 8. Write the following value in standard notation. 3.89 x 104 - 389,000 - 38,900,000 - 389,410 - 38,900

Answers:1. 2.3 x 10^7 2. 7.4 x 10^6 3. 2.1 x 10^-7 4. 3.165 x 10-5 5. 727 x 100 6. True 7. 4,250,000 8. 38,900 ____________ When changing to scientific notation, count the number of places the decimal point moves. When changing to scientific notation - Left is positive - Right is negative When changing from scientific notation - Left is negative - Right is positive

Question:

Answers:17 325/1000 Hope this helps....R (the numbers after the decimal are tenths , hundreths, and thousanths)