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Thread: Numbers

  1. #1
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    Numbers


    Hindu-Arabic numeration system



    The following lists 4 main attributes of this numeration system


    First, it uses 10 digits or symbols that can be used in combination to represent all possible numbers
    The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.


    Second, it groups by tens, probably because we have 10 digits on our two hands. Interestingly enough, the word digit literally means finger or toes.

    In the Hindu-Arabic numeration system,
    ten ones are replaced by one ten,
    ten tens are replaced by one hundred,
    ten hundreds are replaced by one thousand,
    10 one thousand are replaced by 10 thousands,
    and so forth...


    Third, it uses a place value. starting from right to left,

    • the first number represents how many ones there are


    • the second number represents how many tens there are


    • the third number represents how many hundreds there are


    • the fourth number represents how many thousands there are


    • and so on...


    For example, in the numeral 4687, there are 7 ones, 8 tens, 6 hundreds, and 4 thousands

    Finally, the system is additive and multiplicative. The value of a numeral is found by multiplying each place value by its corresponding digit and then adding the resulting products


    Place values: thousand hundred ten one

    Digits 4 6 8 7

    Numeral value is equal to 4 × 1000 + 6 × 100 + 8 × 10 + 7 × 1 = 4000 + 600 + 80 + 7 = 4687


    Notice that the Hindu-Arabic numeration system require requires fewer symbols to represent numbers as opposed to other numeration system.


    Each Hindu-Arabic numeral has a word name. Here is short list:


    0: Zero 10: Ten

    1: One 11: Eleven

    2: Two 15: Fifteen

    3: Three 20: Twenty

    4: Four 30: Thirty-four

    5: Five 40: Fourty

    6: Six 100: One hundred

    7: Seven 590: Five hundred seventy

    8: Eight 5083: Five thousand eighty-three

    9: Nine 56000: Fifty-six thousand




    Numbers from 1 through 12 have unique names


    Numbers from 13 through 19 have "teens" as ending and the ending is blended with names for numbers from 4 through 9


    For numbers from 20 through 99, the tens place is named first followed by a number from 1 through



    Numbers from 100 through 999 are combinations of hundreds and previous names



    Hindu-Arabic numeration system








    Hindu-Arabic numerals, set of 10 symbols—1, 2, 3, 4, 5, 6, 7, 8, 9, 0—that represent numbers in the decimal number system. They originated in India in the 6th or 7th century and were introduced to Europe through the writings of Middle Eastern mathematicians, especially al-Khwarizmi and al-Kindi, about the 12th century. They represented a profound break with previous methods of counting, such as the abacus, and paved the way for the development of algebra.

    Hindu-Arabic numerals | History & Facts | Britannica.com



    Amalfi, Pisa, Genoa and Venice were the first doors and windows through which a permanent contact with the East was established. The sea towns were a means of cultural communication. Arabic numerals, which were to simplify and revolutionise the accounting of merchants, were introduced to the West by the Pisan Leonardo Fibonacci, author of a Liber abbaci, who lived in the late twelfth and early thirteenth centuries. The compass, already known to the Arabs, was adopted by Amalfitani.

    Some claim that it was in Spain that the use of this system began. Probably both Italy and Spain.

    Numbers - we just use them and don't think much about them.

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    MDCLXVI 1666 the ‘Great Fire of London’ occurred.

    All the Roman numerals placed together in order MDCLXVI added up to that fatal year 1666 when the ‘Great Fire of London’ occurred. It is estimated to have destroyed the homes of 70,000 of the city's 80,000 inhabitants.

  3. #3
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    What is the sum of 1 to 1,000,000

    1) What is the sum of the first 100 whole numbers 1 to 100?
    2) What is the sum of the first 1,000 whole numbers 1 to 1,000?
    3) What is the sum of the first 1,000,000 whole numbers 1 to 1,000,000?



    1) What is the sum of the first 100 whole numbers 1 to 100?


    Forwards 1 2 3 4 5 . . . 96 97 98 99 100

    Backwards 100 99 98 97 96 . . . 5 4 3 2 1

    Add 101 101 101 101 101 101 101 101 101 101

    So 100 X 101 = 10,100

    But this is 1 to 100 twice, so divide by 2,

    10,100 ÷ 2 = 5050

    Formula:

    S is the sum of the series, n is the number of terms in the series, in this case 100.
    S = 100 (100 + 1) ÷ 2
    S = n (n +1) ÷ 2



    2) What is the sum of the first 1,000 whole numbers 1 to 1,000?

    easier to use formula

    S = n (n +1) ÷ 2
    = 1000(1000 + 1) ÷ 2
    = ?

    3) What is the sum of the first 1,000,000 whole numbers 1 to 1,000,000?


    Maths is all patterns and formulae.

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