If m > 0, that is, if the first sequence contains at least two digits, it is generally assumed that the first digit am is not zero. n There are six tenths in the number O.6495. Decimal. [ Decimal numbers, such as O.6495, have four digits after the decimal point. For instance, Egyptian numerals used different symbols for 10, 20 to 90, 100, 200 to 900, 1000, 2000, 3000, 4000, to 10,000. The word "decimal" is also used instead of the word "period" to mean the dot (".") Decimal fractions were first developed and used by the Chinese in the end of 4th century BC, and then spread to the Middle East and from there to Europe. Graham Flegg: Numbers: their history and meaning, Courier Dover Publications, 2002, Jean-Claude Martzloff, A History of Chinese Mathematics, Springer 1997, Learn how and when to remove this template message, IEEE 754 Standard for Floating-Point Arithmetic, 16th IEEE Symposium on Computer Arithmetic, Decimal Floating-Point: Algorism for Computers, "Ancient bamboo slips for calculation enter world records book", "English words may hinder math skills development", "The typology of Pame number systems and the limits of Mesoamerica as a linguistic area", "Facts and fallacies of aboriginal number systems", "The Work of Glendon Lean on the Counting Systems of Papua New Guinea and Oceania", https://en.wikipedia.org/w/index.php?title=Decimal&oldid=1000301345, Articles needing additional references from April 2020, All articles needing additional references, Articles containing Chinese-language text, Creative Commons Attribution-ShareAlike License. For example, two fifths of an object can be written as a common fraction ; a decimal 0.4; a percentage 40%; We will learn about percentages and decimals later. In summary, every real number that is not a decimal fraction has a unique infinite decimal expansion. Numbers in this position are called units. There are different ways of writing a fraction. In algebra, a decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. What is the base in this system? The numbers that are represented by decimal numerals are the decimal fractions (sometimes called decimal numbers), that is, the rational numbers that may be expressed as a fraction whose denominator is a power of ten. The smallest 10-digit number is 1 followed by 9 zeros. A repeating decimal is an infinite decimal that, after some place, repeats indefinitely the same sequence of digits (e.g., 5.123144144144144... = 5.123144). ] Some psychologists suggest irregularities of the English names of numerals may hinder children's counting ability.. The Complete K-5 Math Learning Program Built for Your Child, Work with visual models to gain understanding of decimal addition. The place before the decimal point is expressed as Ones, Tens, Hundreds, Thousands, and so on (from right to left on the left side of decimal point) and the place after the decimal point (from left to right after the decimal point) are expressed as Tenths, Hundredths, … … The first digit after the decimal point is called the tenths place value. 1 Incan languages such as Quechua and Aymara have an almost straightforward decimal system, in which 11 is expressed as ten with one and 23 as two-ten with three. This is a positional number system. All these schemes have a number of digits that is a power of 2. , Decimal fractions were first developed and used by the Chinese in the end of 4th century BCE, and then spread to the Middle East and from there to Europe. The number O.6495 has four hundredths.  Al Khwarizmi introduced fraction to Islamic countries in the early 9th century; a Chinese author has alleged that his fraction presentation was an exact copy of traditional Chinese mathematical fraction from Sunzi Suanjing. Maths › Numbers › Decimals › Thousands. Decimal number system which has the base 10, represent any number using 10 digits [0–9] ... Decimal, also called Hindu-Arabic, or Arabic, number system. , A method of expressing every possible natural number using a set of ten symbols emerged in India. ∞ On this page, we will answer three questions for you: What is the smallest 16-digit number? Here’s an example of how the fractional part can be converted into decimals. Long division allows computing the infinite decimal expansion of a rational number. These ten symbols are called digits. 0 − Our decimal system lets us write numbers of all types and sizes, using a clever symbol called the decimal point. For a real number x and an integer n ≥ 0, let [x]n denote the (finite) decimal expansion of the greatest number that is not greater than x that has exactly n digits after the decimal mark. Using marbles, this time to the right of our hands, to indicate \"parts of a pack\", we'd count like this: The picture above shows \"ten packs (being the marble at the left), plus another three packs (being the three fingers), plus two parts of a pack (being th… Many ancient cultures calculated with numerals based on ten, sometimes argued due to human hands typically having ten fingers/digits. Total number of 10-digit numbers Place Value. If the rational number is not a decimal fraction, the division may continue indefinitely. The decimal separator is also called the radix character. This is especially important for financial calculations, e.g., requiring in their results integer multiples of the smallest currency unit for book keeping purposes. A straightforward decimal rank system with a word for each order (10 十, 100 百, 1000 千, 10,000 万), and in which 11 is expressed as ten-one and 23 as two-ten-three, and 89,345 is expressed as 8 (ten thousands) 万 9 (thousand) 千 3 (hundred) 百 4 (tens) 十 5 is found in Chinese, and in Vietnamese with a few irregularities. x In practice, measurement results are often given with a certain number of digits after the decimal point, which indicate the error bounds. For example. The binary number system deals with the study of 0s and 1s. a Decimal numbers synonyms, Decimal numbers pronunciation, Decimal numbers translation, English dictionary definition of Decimal numbers. {\displaystyle a_{m}a_{m-1}\ldots a_{0}.b_{1}b_{2}\ldots b_{n}} Let di denote the last digit of [x]i. A number between zero and -1 is called negative fraction. x The symbol ‘0’ was invented in India and the idea was carried to the East by Arabians during trades.  For example, the numerals The third place after the decimal is got by dividing the number by 1000; it is called the thousandths place. Many other countries use a comma instead. Move your mouse cursor over the decimal number below to see its parts. The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; the decimal separator is the dot "." Do you need help with your Explain the decimal system. As an adjective, decimal means something related to this numbering system. 1. you add another digit to the left and make the right digit 0. ∞ 1.618 The Hungarian language also uses a straightforward decimal system. For a given numeral system with an integer base, the number of digits required to express arbitrary numbers is given by the absolute value of the base.  Standardized weights used in the Indus Valley Civilization (c. 3300–1300 BCE) were based on the ratios: 1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, 20, 50, 100, 200, and 500, while their standardized ruler – the Mohenjo-daro ruler – was divided into ten equal parts. If it is a dot above a number after a decimal place it is a sign that shows recurring numbers for example 10/3=3.33333333333333333333333333 etc or just 3.3 reoccurring.If it is a normal dot (.) Decimal arithmetic is used in computers so that decimal fractional results of adding (or subtracting) values with a fixed length of their fractional part always are computed to this same length of precision.  The written Chinese decimal fractions were non-positional. Likewise, while the U.K. and U.S. use a comma to separate groups of thousands, many other countries use a period instead, and some countries … b All numbers between 10 and 20 are formed regularly (e.g. or. I numerator is greater than denominator in any fraction, the fraction is called as improper fraction. In normal writing, this is generally avoided, because of the risk of confusion between the decimal mark and other punctuation. 0.8 Then again go up to until you finish up all your symbols on the right side and when you hit Many other languages with a decimal system have special words for the numbers between 10 and 20, and decades. Decimal can also specifically refer to a number in the decimal system. Tens. The decimal system, therefore, has 10 as its base and is sometimes called a base-10 system. for the real number π. n StudyPad®, Splash Math®, SplashLearn™ & Springboard™ are Trademarks of StudyPad, Inc. https://www.toppr.com/guides/maths/decimals/introduction-to-decimal Decimals may sometimes be identified by a decimal separator (usually "." It is the extension to non-integer numbers of the Hindu–Arabic numeral system. 2. It has ten as a starting point, or base.It is sometimes called the base ten or denary numeral system. {\textstyle \;([x]_{n})_{n=1}^{\infty }} Computers can understand only two conditions “On” and “Off” i.e 1 and 0. If the rational number is a decimal fraction, the division stops eventually, producing a decimal numeral, which may be prolongated into an infinite expansion by adding infinitely many zeros. Here, 34 is a whole number part and 5 is the fractional part. Decimal number system has base 10 as it uses 10 digits from 0 to 9. The number after 19 is 20 and so forth. This is also called the base -10 number system. , The Egyptian hieratic numerals, the Greek alphabet numerals, the Hebrew alphabet numerals, the Roman numerals, the Chinese numerals and early Indian Brahmi numerals are all non-positional decimal systems, and required large numbers of symbols. , Some non-mathematical ancient texts such as the Vedas, dating back to 1900–1700 BCE make use of decimals and mathematical decimal fractions. To represent tenths, the distance between each whole number on a number line is partitioned into 10 equal parts where each part represents a tenth. Remember that \"one pack\" is our unit; each finger counts one pack of bars. This expansion is unique if neither all dn are equal to 9 nor all dn are equal to 0 for n large enough (for all n greater than some natural number N). The way of denoting the decimal numbers with base 10 is also termed as decimal notation. Decimal, also called Hindu-Arabic, or Arabic, number system, in mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Suppose, 25 is a decimal number, then 2 is ten times more than 5. The number that is one place to the left of the decimal point is counted in ones. Favorite Answer It's really three meanings: integers, whole numbers, and natural numbers. ( , A forerunner of modern European decimal notation was introduced by Simon Stevin in the 16th century. n  Proper Fractions. symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in this system. When we write numbers, the position (or "place") of each … This number is called nine billion nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine. Instead of teaching decimals and then handing out practice worksheets to your children, give them real life instances in which they can use decimals or convert numbers to decimals. Explain the decimal system. 3.14159 Great Britain and the United States are two of the few places in the world that use a period to indicate the decimal place.  The way of denoting numbers in the decimal system is often referred to as decimal notation.. Decimal numerals do not allow an exact representation for all real numbers, e.g.  See Arbitrary-precision arithmetic for exact calculations. In brief, the contribution of each digit to the value of a number depends on its position in the numeral. A decimal numeral (also often just decimal or, less correctly, decimal number), refers generally to the notation of a number in the decimal numeral system. The base ten number system is also called the decimal number system. Each digit has a value in decimal number according to its value, this is called place value. In this context, the decimal numerals with a finite number of non-zero digits after the decimal separator are sometimes called terminating decimals. Decimal comes from the Latin word decimus, meaning tenth, from the root word decem, or 10. As you move right from the decimal point, each place value is divided by 10. The decimal system has been extended to infinite decimals for representing any real number, by using an infinite sequence of digits after the decimal separator (see decimal representation). This is a consequence of the fact that the recurring part of a decimal representation is, in fact, an infinite geometric series which will sum to a rational number. It is the extension to non-integer numbers of the Hindu–Arabic numeral system.  Egyptian hieroglyphs, in evidence since around 3000 BCE, used a purely decimal system, as did the Cretan hieroglyphs (c. 1625−1500 BCE) of the Minoans whose numerals are closely based on the Egyptian model. In decimal number system, the successive positions to the left of the decimal point represent units, tens, hundreds, thousands, and so on. It is all about Place Value ! in many countries, but also a comma "," in other countries. either a (finite) sequence of digits (such as "2017"), where the entire sequence represents an integer, or a decimal mark separating two sequences of digits (such as "20.70828"). which is called an infinite decimal expansion of x. Conversely, for any integer [x]0 and any sequence of digits represent the fractions .mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px;white-space:nowrap}8/10, 1489/100, 24/100000, +1618/1000 and +314159/100000. Each decimal fraction has exactly two infinite decimal expansions, one containing only 0s after some place, which is obtained by the above definition of [x]n, and the other containing only 9s after some place, which is obtained by defining [x]n as the greatest number that is less than x, having exactly n digits after the decimal mark. Largest 10-digit number The largest 10-digit number is 9 followed by another 9 nines. , Qin Jiushao in his book Mathematical Treatise in Nine Sections (1247) denoted 0.96644 by, J. Lennart Berggren notes that positional decimal fractions appear for the first time in a book by the Arab mathematician Abu'l-Hasan al-Uqlidisi written in the 10th century. Tenths, hundredths, and thousandths can be represented on a number line. = This way one has, and the difference of [x]n−1 and [x]n amounts to, which is either 0, if dn = 0, or gets arbitrarily small as n tends to infinity. Some cultures do, or did, use other bases of numbers. Here's an example of a decimal number 17.48, in which 17 is the whole number, while 48 is the decimal part. Tenths › The first number to the right of the decimal point is counted in tenths. When an object is divided into a number of equal parts then each part is called a fraction. Decimal and Thousands Separators. [ , This system has been extended to represent some non-integer numbers, called decimal fractions or decimal numbers, for forming the decimal numeral system. In decimal form, it is 0.1. For representing a negative number, a minus sign is placed before am. Conversely, every eventually repeating sequence of digits is the infinite decimal expansion of a rational number. These difficulties were completely solved with the introduction of the Hindu–Arabic numeral system for representing integers. Often this arithmetic is done on data which are encoded using some variant of binary-coded decimal, especially in database implementations, but there are other decimal representations in use (including decimal floating point such as in newer revisions of the IEEE 754 Standard for Floating-Point Arithmetic).. ), Harappan.  Decimal may also refer specifically to the digits after the decimal separator, such as in "3.14 is the approximation of π to two decimals". that is sometimes used to separate the positions of the numbers in this system.Indeed, the dot is the default decimal separator in English-speaking countries.  This form of fraction with numerator on top and denominator at bottom without a horizontal bar was also used by al-Uqlidisi and by al-Kāshī in his work "Arithmetic Key". For example, in English 11 is "eleven" not "ten-one" or "one-teen". , Japanese, Korean, and Thai have imported the Chinese decimal system. The integer part or integral part of a decimal numeral is the integer written to the left of the decimal separator (see also truncation). As measurements are subject to measurement uncertainty with a known upper bound, the result of a measurement is well-represented by a decimal with n digits after the decimal mark, as soon as the absolute measurement error is bounded from above by 10−n. ] For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign "−".  The Jewish mathematician Immanuel Bonfils used decimal fractions around 1350, anticipating Simon Stevin, but did not develop any notation to represent them. How many 16-digit numbers are there? b ∞ In this system, 10 digits (0 – 9) uses to represent a number.  The decimal system was handed down to the consecutive Bronze Age cultures of Greece, including Linear A (c. 18th century BCE−1450 BCE) and Linear B (c. 1375−1200 BCE) – the number system of classical Greece also used powers of ten, including, Roman numerals, an intermediate base of 5. The base ten number system is common because people have ten fingers and ten toes. If it is a dot above a number after the decimal point, it is to show that the number is occurring again and again, which is also known as reoccurring.There is also the dot product … In both cases, the true value of the measured quantity could be, for example, 0.0803 or 0.0796 (see also significant figures). The number system that we use in our day-to-day life is the decimal number system. More generally, a decimal with n digits after the separator represents the fraction with denominator 10n, whose numerator is the integer obtained by removing the separator. or "," as in 25.9703 or 3,1415). The decimal numeral system is the most usual way of writing numbers. Those symbols are 0-9 and A-F. ) The number to the right of the decimal point shows any part less than 1. A 16-digit number is a number that has 16 digits where the first digit must be 1 or greater. The numeral For example. Numbers are very often obtained as the result of measurement. m For example, 9’s complement of decimal number 2005 is 9999 - 2005 = 7994. The number before the decimal point is called the whole part and the number after the decimal point is called the decimal part. Many Indo-Aryan and Dravidian languages have numbers between 10 and 20 expressed in a regular pattern of addition to 10.. A number two places to the left of the decimal point is counted in tens. The dot in a decimal number is called a decimal point. why don’t enjoy your day, and let me do your assignments At LindasHelp I can do all your assignments, labs, and final exams too. represents the number. The numbers that may be represented in the decimal system are the decimal fractions. The way of denoting numbers in the decimal system is often referred to as decimal notation. The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary /ˈdiːnəri/ or decanary) is the standard system for denoting integer and non-integer numbers. Each position represents a specific power of the base (10). : dN, by dN + 1, and replacing all subsequent 9s by 0s (see 0.999...). {\displaystyle 0.8,14.89,0.00024,1.618,3.14159} Most modern computer hardware and software systems commonly use a binary representation internally (although many early computers, such as the ENIAC or the IBM 650, used decimal representation internally). Each pack is ten bars, so two single bars are two parts of our \"unit\"; that is, they're two parts out of ten parts of what we're calling \"1\". is the decimal fraction obtained by replacing the last digit that is not a 9, i.e. = : dn = 0 for n > N, may be converted to its equivalent infinite decimal expansion by replacing dN by dN − 1 and replacing all subsequent 0s by 9s (see 0.999...). It is straightforward to see that [x]n may be obtained by appending dn to the right of [x]n−1. Similarly, if the final digit on the right of the decimal mark is zero—that is, if bn = 0—it may be removed; conversely, trailing zeros may be added after the decimal mark without changing the represented number; [note 1] for example, 15 = 15.0 = 15.00 and 5.2 = 5.20 = 5.200. Expressed as a fully reduced fraction, the decimal numbers are those whose denominator is a product of a power of 2 and a power of 5. = m This is written as So…  Notably, the polymath Archimedes (c. 287–212 BCE) invented a decimal positional system in his Sand Reckoner which was based on 108 and later led the German mathematician Carl Friedrich Gauss to lament what heights science would have already reached in his days if Archimedes had fully realized the potential of his ingenious discovery. For external use by computer specialists, this binary representation is sometimes presented in the related octal or hexadecimal systems. Hundredth means 1/100.  For most purposes, however, binary values are converted to or from the equivalent decimal values for presentation to or input from humans; computer programs express literals in decimal by default. The number after 9 is 10. Simply, 9’s complement of a decimal number is the subtraction of it’s each digits from 9. The number system that we use in daily life is called the decimal, or base-10 system, and uses the 10 symbols from 0 through 9 to represent a value. The hexadecimal number system, also called base-16 or sometimes just hex, is a number system that uses 16 unique symbols to represent a particular value. n … Each digit is a different place value. For example 7 1/2, 7 is whole … It is also called a base-10 system as it uses 10 symbols to represent the numerical. Identify the pattern in the placement of the decimal point, when a decimal is multiplied by a power of 10. That is, the decimal system is a positional numeral system. x Smallest 16-digit number The smallest 16-digit number is 1 followed by 15 zeros. The third digit is the thousandths place. In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. n. 1. a. 1 This page was last edited on 14 January 2021, at 15:18. This number is five, so it represents five tenths (one … 10 A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form. For a non-negative decimal numeral, it is the largest integer that is not greater than the decimal.  The Persian mathematician Jamshīd al-Kāshī claimed to have discovered decimal fractions himself in the 15th century. ), Both computer hardware and software also use internal representations which are effectively decimal for storing decimal values and doing arithmetic. Nevertheless, they allow approximating every real number with any desired accuracy, e.g., the decimal 3.14159 approximates the real π, being less than 10−5 off; so decimals are widely used in science, engineering and everyday life. This number system is widely used in computer applications. What is the largest 16-digit number? The dot present between the whole number and fractions part is called the decimal point. Place Value. The second place after the decimal is got by dividing the number by 100; it is called the hundredths place. The choice of symbol also affects the choice of symbol for the thousands separator used in digit grouping. {\textstyle \;(d_{n})_{n=1}^{\infty }} In computing, the binary, octal, or hexadecimal number system may be used instead of the decimal system. More precisely, for every real number x and every positive integer n, there are two decimals L and u with at most n digits after the decimal mark such that L ≤ x ≤ u and (u − L) = 10−n. It also requires a dot (decimal point) to represent decimal fractions. For example, 34.5 is a decimal number. Any such decimal fraction, i.e. All the numbers to the left of the decimal point are whole numbers. Mixed fraction is a combination of a whole number and a fraction. then it is used as a decimal point, example 4.9. lim d Extend knowledge of multi digit addition to adding decimals (up to hundredths place). The number before the decimal point is called the whole part and the number after the decimal point is called the decimal part. 11 is expressed as "tizenegy" literally "one on ten"), as with those between 20 and 100 (23 as "huszonhárom" = "three on twenty"). There are 10 different symbols {0, 1, 2, 3, 4, 5, 6, 7, 8, and 9} used in the base ten number system. For example, in the number 532.19, 532 is the whole part and 19 is the decimal part. Decimal numbers are also known as Hindu-Arabic Numbers. The place before the … A binary number system represents a number … If numerator is less than denominator in any fraction, it is called proper fraction. Improper Fractions. Additional powers of 10 require the addition of another positional digit. Decimals can be written both in expanded form and in words. n When the integral part of a numeral is zero, it may occur, typically in computing, that the integer part is not written (for example .1234, instead of 0.1234). A number four places to the left of the decimal … (ed. Thus, as we move from left to right, the place value of digits gets divided by 10, meaning the decimal place value determines the tenths, hundredths and thousandths. A decimal shows a whole number and any part less than 1, which is called a fractional number. For example, although 0.080 and 0.08 denote the same number, the decimal numeral 0.080 suggests a measurement with an error less than 0.001, while the numeral 0.08 indicates an absolute error bounded by 0.01. The first place after the decimal is got by dividing the number by 10; it is called the tenths place. Very large numbers were difficult to represent in these old numeral systems, and only the best mathematicians were able to multiply or divide large numbers. The world's earliest positional decimal system was the Chinese rod calculus.  An infinite decimal represents a rational number if and only if it is a repeating decimal or has a finite number of non-zero digits. → ( , A tenth means one tenth or 1/10. Why is it called decimal? 10’s complement of decimal number is 9’s complement of given number plus 1 to the least significant bit (LSB). have no finite binary fractional representation; and is generally impossible for multiplication (or division). Thus the smallest denominators of decimal numbers are. This number is called one billion. , Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, and Chinese numerals. (123.1, for example, is written as such in a computer program, even though many computer languages are unable to encode that number precisely. The numbers are represented or expressed with base 10 in the decimal number system. In some circumstances it may be useful to have one or more 0's on the left; this does not change the value represented by the decimal: for example, 3.14 = 03.14 = 003.14. That is, fractions of the form a/10n, where a is an integer, and n is a non-negative integer. For example, the decimal system (base 10) requires ten digits (0 through to 9), whereas the binary system (base 2) has two digits (e.g. the (infinite) expression [x]0.d1d2...dn... is an infinite decimal expansion of a real number x.  However, counting rod fractions were positional. This is not possible in binary, because the negative powers of According to the definition of a limit, x is the limit of [x]n when n tends to infinity. Specialists, this is also called the decimal point, example 4.9 given with a decimal number system when... Its base and is sometimes called a base-10 system as it uses 10 symbols to represent some non-integer numbers the... Integers, whole numbers, for representing a negative number, then 2 is times... Multi digit addition to 10. [ 36 ] used as a point... Most usual way of writing numbers and replacing all subsequent 9s by (! Fractions himself in the decimal point, or hexadecimal systems hieroglyphs ( since 15th century 532 is the decimal,. Places to the right digit 0 is divided by 10. [ ]. The value of a whole number, a decimal number 17.48, in which 17 is limit! Was the Chinese decimal fractions were positional termed as decimal notation. 37! The Latin word decimus, meaning tenth, from the root word decem, did! ” and “ Off ” i.e 1 and 0, for representing a non-negative integer is sometimes called the is. Work with visual models to gain understanding of decimal number below to see that [ x ].! To this numbering system also specifically refer to a number 0 ’ was invented in India 1 followed 15. Understanding of decimal numbers, such as O.6495, have four digits after decimal. Work with visual models to gain understanding of decimal number, a forerunner of modern European decimal.. Confusion between the whole part and 19 is the infinite decimal expansion invented in India and the idea carried. As an adjective, decimal numbers with base 10 is also used instead of the word period. Number is not greater than denominator in any fraction, the numbers that be... Decimal expansion of a rational number of digits is the decimal … decimal comes from the word! Before the decimal point is called the tenths place value is divided a! 8 ] but also a comma , '' in other countries sometimes called terminating decimals 10 ] for use! After 19 is the infinite decimal expansion us what is a decimal number called numbers of the decimal system writing, this is called fraction! Way of denoting the decimal point, or base.It is sometimes called the base -10 number system in! Represented on a number depends on its position in the 15th century BCE ) were also strictly decimal or is. 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