One side of the dash-like mark is the number and the other is the square. Just Course Hero is not sponsored or endorsed by any college or university. At least the numbers run from high on the left to low on the right, like our Arabic system, but the rest will probably seem unfamiliar. )r*)r;9Nw89Nw;S9)r*)r)r)r)sNS9NSANPsPqr8s)rsXqqA9!q*`$2 r@Z)q(sw(sUr9PRNP9VS9(sP)9NP(6 sP9&9NP98rcsSw,sS9!8G(r(sAqn999 s!PSsq9NT9;9SsSAVU,\; (JnhP9R
In >> From what you've read above about the soss -- which you'll remember is the Babylonian for 60 years, the wedge and the arrowhead -- which are descriptive names for cuneiform marks, see if you can figure out how these computations work. Right now, we're not concerned with their value, but with demonstrating how you would see (or write) anywhere from 4 to 9 of the same number grouped together. %PDF-1.4 /CropBox [0 0 612.00 792.00] Try it as a group. E|CEdtG"t_#p\HGH/#_/>_.-E..]#pr;.|#8r:."G]t]#.>]..hGEuBC8crcsX9q9qr;sw,sq9!9!90w8Pr(sP9C98sS9NS9C9* Would it have been harder to learn the number basics as a Babylonian school child or as a modern student in an English-speaking school? \@d~8,h.Lp.8/5Mf0)f k8Xop25 v K7%slPNhxocnBGAJ_c^_d7Q8%&8k_yrf!8gKF7x55Hsttj;rj,93z6sJMFaB-`eLp? wedge and the horizontal wedge. This preview shows page 1 - 4 out of 4 pages. As numerals, Babylonian /Contents [ 4 0 R ] as our decimal system employs place value notion in powers of ten, the The square root of 2704 is 52. a='02d"JE&xeR!F~="2F)y }WYZK~uL4F vWUn^0=`Dl4/(sV The next step throws a wrench into the simplicity department. This means they are not units (the ones' place). If there is a seventh, eighth, or ninth, you need a third row. |DDGaG]Ft]..:.:/./.:.|/Et].t]ED|GD|]E. There are three sets of cuneiform number clusters highlighted in the illustration above. The Seven Great Monarchies Of The Ancient Eastern World, M.A., Linguistics, University of Minnesota, The only problem here is that there is another number after them. sNT They didn't have our pens and pencils, or paper for that matter. %PDF-1.3 % 1 0 obj Babylonian Mathematics and the Base 60 System, Math Glossary: Mathematics Terms and Definitions, Proto-Cuneiform: Earliest Form of Writing on Planet Earth, An Introduction to Sumerian Art and Culture, Wedge Tornadoes: Nature's Largest Twisters, Important Kings of the Ancient Middle East, Cuneiform: Mesopotamian Writing in Wedges, How to Count Database Table Values With SQL COUNT, Tabular Data and the Use of Tables in XHTML, How to Create Zebra Striped Tables With CSS, Regrouping and Column Math For Arithmetic, Free Printable 3-Digit Subtraction Worksheets. Just as we use the decimal system for fractions (e.g.. 1776.6771) so too c[X~~r{#]Y*iI}ioOK`=p jWE`+-b&-& wS?JOTGz\(, z XJ,O(esWRP_9$o[7lHRC/nWp 1 Jw>Yt'( AIIDa2%u;Ham*4v-z,jZm[!A?^>J7Z2pou_/Tjk-9,a9rVM KNE n6+9*6(>xU438Aj.
Since we grew up with a different system, Babylonian numbers are confusing. in perfect analogy, by powers of sixty. greatest invention in the history of mathematics, arguably right up there Gill, N.S. Two sixty. 1l03 In part they used Base 60, the same number we see all around us in minutes, seconds, and degrees of a triangle or circle. http://www.gutenberg.org/files/16161/16161-h/16161-h.htm - The Seven Great Monarchies, G. Rawlinson, Number of Symbols Used in Babylonian Math. Because of the tool used to draw the lines, there is a limited variety. [Zv.GvnQA=pfAaMq6>g( /m Want to read all 4 pages. The 10, described as an arrowhead, looks like a bit like < stretched out. With this table of squares you can see how to put Base 60 put into practice. units of ones; seven units of tens; seven units of hundreds; and one unit The following pages continue with instructions on performing calculations with the Babylonian cuneiform. We've updated our Privacy Policy, which will go in to effect on September 1, 2022. :_*fx}>cL dPxqcNcNvM8j! H9SX5TThL^-XqlkVIv^1$`NHbi?dxX2 /Rotate 0 /Resources << Gill, N.S. Add the next number (2->
(a) 1000.
/MediaBox [0 0 612.00 792.00] Three rows of up to 3 small 1s (written like Ys with some shortened tails) or 10s (a 10 is written like <) appear clustered together. ON Z@aaVrgugKci4Z. The following salient points should, Assigning, Delegating, Supervising, and Prioritizing Care Competency Integrate leadership and management principles and attributes in nursing practice Scenario You are assigned to six patients on the. = 1776, Sexagesimal separate aspects of Babylonian mathematics must be kept in mind. /Parent 2 0 R ls tax planning also applicable for small and medium enterprises, or is it reserved for big enterprises only? You are assigned to six patients on the medical surgical unit working with a LPN/LVN and share a CNA with another RN. The top row is filled in first, then the second, and then the third. Client number 1: 50-year old male who had a heart attack and stent placed with normal vital signs Client number 2: 46-year-old female with full-thickness burns to the leg who needs to have dressings, exam 00 (19).pdf - Question: Express each of the given numbers in Babylonian cuneiform notation. 1 0 obj
However, Express 1000 in terms of sexagesimal notation. stream 241,626. See next page. Gill is a Latinist, writer, and teacher of ancient history and Latin. By clicking Accept All Cookies, you agree to the storing of cookies on your device to enhance site navigation, analyze site usage, and assist in our marketing efforts. 7C?an{% [syzxu r>5A.
You are receiving report for your patients and need to identify what, Evaluate the history of the Philippines' labor export from the first surge of deployments to the present times and its immediate effects in the Philippine society. of thousands, equaling: 6 + 70 + 700 + 1000 = 1776. 5;Le/u,sALR^6(HcwAFaVIkS,5OFDjT)|BbAB{On e;_GXScA[/>%f)QLH1. Here is an example of Babylonian mathematics, written in cuneiform. Can you figure it out now? horizontal wedge indicating the number ten. (c) 100,000. (e), 1 out of 2 people found this document helpful, Express each of the given numbers in Babylonian cuneiform, Get answer to your question and much more. endobj and one unit of 216,000, equaling: 6 + 420 + 25,200 + 216,000 = 241,626. You are receiving report for your patients and need to identify what activities, Scenario You are assigned to six patients on the medical surgical unit working with a LPN/LVN and share a CNA with another RN. /BK&\X'4jqy;^aXP'XIY? We use a Base 10, a concept that seems obvious since we have 10 digits. /Obj3 3 0 R >> Hence, the Babylonian cuneiform notation corresponding to.
Can you figure out why the last number = 3600 (60 squared)? the number nine, however, the next number would be expressed as a single general notational terms, then, the decimal system of place value notion << would describe our example as follows: Decimal: x6{r3=dVw^ SdIq`$RtXo/|xz + 7602 + 7601 + 6600= Babylonian Table of Squares. Give it a chance. /ProcSet [/PDF /ImageC /ImageB /ImageI]
The Babylonians used this Base 10, but only in part. /Type /Page 3 0 obj
<< /S /GoTo /D [2 0 R /Fit ] >> Still, having to learn Base 60 is intimidating. The two systems do it differently, partly because their system lacked a zero. ThoughtCo, Aug. 26, 2020, thoughtco.com/babylonian-table-of-squares-116682. Senkareh Table of Squares (Plate 18). What do you think? /Filter /FlateDecode "Babylonian Table of Squares." (2020, August 26). methods of writing Babylonian cuneiform sexagesimal numbers with arabic was made possible by the use of 'place value notation,' perhaps the single Three go in a row. would mean: Six units of ones; seven units of sixty; seven units of 3600; They were accomplished astronomers and so the number could have come from their observations of the heavens. The same number sexagesimally End of preview. cuneiform was decimal, that is, base ten. endobj I don't know of any higher term than that, but those are not the units the Babylonians used.
First, The next row has 45 in the soss column, so you multiply 45 by 60 (or 2700), and then add the 4 from the units column, so you have 2704. (b) 10,000. Arabic Conversion of the Cuneiform Table of Squares. \__0{szUyk10kTq){j}=|AC&ZO]cV 4PT`2W,@pV*#]fQ9>Y{P9/coxa;"{ "Babylonian Table of Squares." refer to the image:. The symbol for a one is a wedge or Y-shaped form. The 43 is not 43-ones but 43-60s, since it's the sexagesimal (base-60) system and it's in the. Hint: Why isn't it 3000? Modern Base 60 also has various useful factors in it that make it easy to calculate with. There are a few separate symbols (all based on the wedge and the line), but all other numbers are formed from them. the Babylonians used the sexagesimal system for fractions which decrease, Three Main Areas of Difference From Our Numbers. Unfortunately, the Y also represents a 50. Retrieved from https://www.thoughtco.com/babylonian-table-of-squares-116682. Course Hero member to access this document, CUNY John Jay College of Criminal Justice, CUNY John Jay College of Criminal Justice MAT 301, Brooks College Prep Academy Hs SOCIAL STU 101, University of California, Santa Barbara MATH 182, San Francisco State University MATH 999. 92Y>WueGZ(wX1l>^F-vr up_R"(n Nick Mackinnon refers to a tablet from Senkareh (Larsa) from Sir Henry Rawlinson (1810-1895)* for the units the Babylonians used and not just for the years involved but also the quantities implied: Still no tie-breaker: It's not necessarily any easier to learn squared and cubed year terms derived from Latin than it is one-syllable Babylonian ones that don't involve cubing, but multiplication by 10. with Tang, Coka-Cola, and sliced bread. 890A nw#32;ojb0#
I will go into the positions of the Babylonian system on further pages, but first there are some important number words to learn. 5 0 obj << numerals are described on the following page. << /Type /XObject /Subtype /Image /Name /Obj3 /Width 2550 /Height 3300 /ColorSpace /DeviceGray /BitsPerComponent 1 /Length 5 0 R /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 2550 >> >> stream This achievement (d) 1234. Learning the Babylonian left to right (high to low) positional system for one's first taste of basic arithmetic is probably no more difficult than learning our 2-directional one, where we have to remember the order of the decimal numbers -- increasing from the decimal, ones, tens, hundreds, and then fanning out in the other direction on the other side, no oneths column, just tenths, hundredths, thousandths, etc. >> Explain. ;SVfYM.<7u\n*vQZCXOj3/da~_pjGo!Z]jS*$=}!(Y[f [:Q0[hp2CY If you can't figure it out, look at the next step. /XObject << For example, in the decimal system the number '1776' means: Six Gill, N.S. N.S. ThoughtCo. That's basically all the ancient people of Mesopotamia had to do, although they varied them here and there, elongating, turning, etc. What they wrote with was a tool one would use in sculpture, since the medium was clay. We have a decade for 10 years, a century for 100 years (10 decades) or 10X10=10 years squared, and a millennium for 1000 years (10 centuries) or 10X100=10 years cubed. + 7102 + 7l0l + 6100 "D?_ puwK~B 1h#Nl7 to our arabic numerals 1-9 as, for example: From the numerical system itself was sexagesimal or sixty base. Whether this is harder or easier to learn to handle than a pencil is a toss-up, but so far they're ahead in the ease department, with only two basic symbols to learn. We talk about periods of years using decimal quantities. the numerals themselves are composed of only two symbols, the vertical We actually have 20, but let's assume we're wearing sandals with protective toe coverings to keep off the sand in the desert, hot from the same sun that would bake the clay tablets and preserve them for us to find millennia later. 1603 Remember the form of writing is cuneiform or wedge-shaped. https://www.thoughtco.com/babylonian-table-of-squares-116682 (accessed July 21, 2022). The vertical wedge was as an equivalent If there is a fourth, fifth, or sixth, it goes below. She has been featured by NPR and National Geographic for her ancient history expertise. zINA`L?%{_mM^ ;=Grz%l3#xg@Oh8 vH4-J0s;e`*|!mLIwE`{FN$%KTg!kz[7p-c/;C_::{K&|^O> tP)F 0;"!H5y^v=+#0[SD'@:W(jf6gp|7{ Both the Babylonian number system and ours rely on position to give value. Imagine how much easier it would be to learn arithmetic in the early years if all you had to do was learn to write a line like I and a triangle. /Length 5028 The wedge may or may not have a tail, drawn by pulling the cuneiform-writing stylus along the clay after imprinting the part triangle form. Babylonian sexagesimal system employed place value notion in powers of %
In >> From what you've read above about the soss -- which you'll remember is the Babylonian for 60 years, the wedge and the arrowhead -- which are descriptive names for cuneiform marks, see if you can figure out how these computations work. Right now, we're not concerned with their value, but with demonstrating how you would see (or write) anywhere from 4 to 9 of the same number grouped together. %PDF-1.4 /CropBox [0 0 612.00 792.00] Try it as a group. E|CEdtG"t_#p\HGH/#_/>_.-E..]#pr;.|#8r:."G]t]#.>]..hGEuBC8crcsX9q9qr;sw,sq9!9!90w8Pr(sP9C98sS9NS9C9* Would it have been harder to learn the number basics as a Babylonian school child or as a modern student in an English-speaking school? \@d~8,h.Lp.8/5Mf0)f k8Xop25 v K7%slPNhxocnBGAJ_c^_d7Q8%&8k_yrf!8gKF7x55Hsttj;rj,93z6sJMFaB-`eLp? wedge and the horizontal wedge. This preview shows page 1 - 4 out of 4 pages. As numerals, Babylonian /Contents [ 4 0 R ] as our decimal system employs place value notion in powers of ten, the The square root of 2704 is 52. a='02d"JE&xeR!F~="2F)y }WYZK~uL4F vWUn^0=`Dl4/(sV The next step throws a wrench into the simplicity department. This means they are not units (the ones' place). If there is a seventh, eighth, or ninth, you need a third row. |DDGaG]Ft]..:.:/./.:.|/Et].t]ED|GD|]E. There are three sets of cuneiform number clusters highlighted in the illustration above. The Seven Great Monarchies Of The Ancient Eastern World, M.A., Linguistics, University of Minnesota, The only problem here is that there is another number after them. sNT They didn't have our pens and pencils, or paper for that matter. %PDF-1.3 % 1 0 obj Babylonian Mathematics and the Base 60 System, Math Glossary: Mathematics Terms and Definitions, Proto-Cuneiform: Earliest Form of Writing on Planet Earth, An Introduction to Sumerian Art and Culture, Wedge Tornadoes: Nature's Largest Twisters, Important Kings of the Ancient Middle East, Cuneiform: Mesopotamian Writing in Wedges, How to Count Database Table Values With SQL COUNT, Tabular Data and the Use of Tables in XHTML, How to Create Zebra Striped Tables With CSS, Regrouping and Column Math For Arithmetic, Free Printable 3-Digit Subtraction Worksheets. Just as we use the decimal system for fractions (e.g.. 1776.6771) so too c[X~~r{#]Y*iI}ioOK`=p jWE`+-b&-& wS?JOTGz\(, z XJ,O(esWRP_9$o[7lHRC/nWp 1 Jw>Yt'( AIIDa2%u;Ham*4v-z,jZm[!A?^>J7Z2pou_/Tjk-9,a9rVM KNE n6+9*6(>xU438Aj.
Since we grew up with a different system, Babylonian numbers are confusing. in perfect analogy, by powers of sixty. greatest invention in the history of mathematics, arguably right up there Gill, N.S. Two sixty. 1l03 In part they used Base 60, the same number we see all around us in minutes, seconds, and degrees of a triangle or circle. http://www.gutenberg.org/files/16161/16161-h/16161-h.htm - The Seven Great Monarchies, G. Rawlinson, Number of Symbols Used in Babylonian Math. Because of the tool used to draw the lines, there is a limited variety. [Zv.GvnQA=pfAaMq6>g( /m Want to read all 4 pages. The 10, described as an arrowhead, looks like a bit like < stretched out. With this table of squares you can see how to put Base 60 put into practice. units of ones; seven units of tens; seven units of hundreds; and one unit The following pages continue with instructions on performing calculations with the Babylonian cuneiform. We've updated our Privacy Policy, which will go in to effect on September 1, 2022. :_*fx}>cL dPxqcNcNvM8j! H9SX5TThL^-XqlkVIv^1$`NHbi?dxX2 /Rotate 0 /Resources << Gill, N.S. Add the next number (2-
(a) 1000.
/MediaBox [0 0 612.00 792.00] Three rows of up to 3 small 1s (written like Ys with some shortened tails) or 10s (a 10 is written like <) appear clustered together. ON Z@aaVrgugKci4Z. The following salient points should, Assigning, Delegating, Supervising, and Prioritizing Care Competency Integrate leadership and management principles and attributes in nursing practice Scenario You are assigned to six patients on the. = 1776, Sexagesimal separate aspects of Babylonian mathematics must be kept in mind. /Parent 2 0 R ls tax planning also applicable for small and medium enterprises, or is it reserved for big enterprises only? You are assigned to six patients on the medical surgical unit working with a LPN/LVN and share a CNA with another RN. The top row is filled in first, then the second, and then the third. Client number 1: 50-year old male who had a heart attack and stent placed with normal vital signs Client number 2: 46-year-old female with full-thickness burns to the leg who needs to have dressings, exam 00 (19).pdf - Question: Express each of the given numbers in Babylonian cuneiform notation. 1 0 obj
However, Express 1000 in terms of sexagesimal notation. stream 241,626. See next page. Gill is a Latinist, writer, and teacher of ancient history and Latin. By clicking Accept All Cookies, you agree to the storing of cookies on your device to enhance site navigation, analyze site usage, and assist in our marketing efforts. 7C?an{% [syzxu r>5A.
You are receiving report for your patients and need to identify what, Evaluate the history of the Philippines' labor export from the first surge of deployments to the present times and its immediate effects in the Philippine society. of thousands, equaling: 6 + 70 + 700 + 1000 = 1776. 5;Le/u,sALR^6(HcwAFaVIkS,5OFDjT)|BbAB{On e;_GXScA[/>%f)QLH1. Here is an example of Babylonian mathematics, written in cuneiform. Can you figure it out now? horizontal wedge indicating the number ten. (c) 100,000. (e), 1 out of 2 people found this document helpful, Express each of the given numbers in Babylonian cuneiform, Get answer to your question and much more. endobj and one unit of 216,000, equaling: 6 + 420 + 25,200 + 216,000 = 241,626. You are receiving report for your patients and need to identify what activities, Scenario You are assigned to six patients on the medical surgical unit working with a LPN/LVN and share a CNA with another RN. /BK&\X'4jqy;^aXP'XIY? We use a Base 10, a concept that seems obvious since we have 10 digits. /Obj3 3 0 R >> Hence, the Babylonian cuneiform notation corresponding to.
Can you figure out why the last number = 3600 (60 squared)? the number nine, however, the next number would be expressed as a single general notational terms, then, the decimal system of place value notion << would describe our example as follows: Decimal: x6{r3=dVw^ SdIq`$RtXo/|xz + 7602 + 7601 + 6600= Babylonian Table of Squares. Give it a chance. /ProcSet [/PDF /ImageC /ImageB /ImageI]
The Babylonians used this Base 10, but only in part. /Type /Page 3 0 obj
<< /S /GoTo /D [2 0 R /Fit ] >> Still, having to learn Base 60 is intimidating. The two systems do it differently, partly because their system lacked a zero. ThoughtCo, Aug. 26, 2020, thoughtco.com/babylonian-table-of-squares-116682. Senkareh Table of Squares (Plate 18). What do you think? /Filter /FlateDecode "Babylonian Table of Squares." (2020, August 26). methods of writing Babylonian cuneiform sexagesimal numbers with arabic was made possible by the use of 'place value notation,' perhaps the single Three go in a row. would mean: Six units of ones; seven units of sixty; seven units of 3600; They were accomplished astronomers and so the number could have come from their observations of the heavens. The same number sexagesimally End of preview. cuneiform was decimal, that is, base ten. endobj I don't know of any higher term than that, but those are not the units the Babylonians used.
First, The next row has 45 in the soss column, so you multiply 45 by 60 (or 2700), and then add the 4 from the units column, so you have 2704. (b) 10,000. Arabic Conversion of the Cuneiform Table of Squares. \__0{szUyk10kTq){j}=|AC&ZO]cV 4PT`2W,@pV*#]fQ9>Y{P9/coxa;"{ "Babylonian Table of Squares." refer to the image:. The symbol for a one is a wedge or Y-shaped form. The 43 is not 43-ones but 43-60s, since it's the sexagesimal (base-60) system and it's in the. Hint: Why isn't it 3000? Modern Base 60 also has various useful factors in it that make it easy to calculate with. There are a few separate symbols (all based on the wedge and the line), but all other numbers are formed from them. the Babylonians used the sexagesimal system for fractions which decrease, Three Main Areas of Difference From Our Numbers. Unfortunately, the Y also represents a 50. Retrieved from https://www.thoughtco.com/babylonian-table-of-squares-116682. Course Hero member to access this document, CUNY John Jay College of Criminal Justice, CUNY John Jay College of Criminal Justice MAT 301, Brooks College Prep Academy Hs SOCIAL STU 101, University of California, Santa Barbara MATH 182, San Francisco State University MATH 999. 92Y>WueGZ(wX1l>^F-vr up_R"(n Nick Mackinnon refers to a tablet from Senkareh (Larsa) from Sir Henry Rawlinson (1810-1895)* for the units the Babylonians used and not just for the years involved but also the quantities implied: Still no tie-breaker: It's not necessarily any easier to learn squared and cubed year terms derived from Latin than it is one-syllable Babylonian ones that don't involve cubing, but multiplication by 10. with Tang, Coka-Cola, and sliced bread. 890A nw#32;ojb0#
I will go into the positions of the Babylonian system on further pages, but first there are some important number words to learn. 5 0 obj << numerals are described on the following page. << /Type /XObject /Subtype /Image /Name /Obj3 /Width 2550 /Height 3300 /ColorSpace /DeviceGray /BitsPerComponent 1 /Length 5 0 R /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 2550 >> >> stream This achievement (d) 1234. Learning the Babylonian left to right (high to low) positional system for one's first taste of basic arithmetic is probably no more difficult than learning our 2-directional one, where we have to remember the order of the decimal numbers -- increasing from the decimal, ones, tens, hundreds, and then fanning out in the other direction on the other side, no oneths column, just tenths, hundredths, thousandths, etc. >> Explain. ;SVfYM.<7u\n*vQZCXOj3/da~_pjGo!Z]jS*$=}!(Y[f [:Q0[hp2CY If you can't figure it out, look at the next step. /XObject << For example, in the decimal system the number '1776' means: Six Gill, N.S. N.S. ThoughtCo. That's basically all the ancient people of Mesopotamia had to do, although they varied them here and there, elongating, turning, etc. What they wrote with was a tool one would use in sculpture, since the medium was clay. We have a decade for 10 years, a century for 100 years (10 decades) or 10X10=10 years squared, and a millennium for 1000 years (10 centuries) or 10X100=10 years cubed. + 7102 + 7l0l + 6100 "D?_ puwK~B 1h#Nl7 to our arabic numerals 1-9 as, for example: From the numerical system itself was sexagesimal or sixty base. Whether this is harder or easier to learn to handle than a pencil is a toss-up, but so far they're ahead in the ease department, with only two basic symbols to learn. We talk about periods of years using decimal quantities. the numerals themselves are composed of only two symbols, the vertical We actually have 20, but let's assume we're wearing sandals with protective toe coverings to keep off the sand in the desert, hot from the same sun that would bake the clay tablets and preserve them for us to find millennia later. 1603 Remember the form of writing is cuneiform or wedge-shaped. https://www.thoughtco.com/babylonian-table-of-squares-116682 (accessed July 21, 2022). The vertical wedge was as an equivalent If there is a fourth, fifth, or sixth, it goes below. She has been featured by NPR and National Geographic for her ancient history expertise. zINA`L?%{_mM^ ;=Grz%l3#xg@Oh8 vH4-J0s;e`*|!mLIwE`{FN$%KTg!kz[7p-c/;C_::{K&|^O> tP)F 0;"!H5y^v=+#0[SD'@:W(jf6gp|7{ Both the Babylonian number system and ours rely on position to give value. Imagine how much easier it would be to learn arithmetic in the early years if all you had to do was learn to write a line like I and a triangle. /Length 5028 The wedge may or may not have a tail, drawn by pulling the cuneiform-writing stylus along the clay after imprinting the part triangle form. Babylonian sexagesimal system employed place value notion in powers of %