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A Story of Numbers

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Page 51: We need to tackle these questions without the use of the number names or written numbers of the Hindu number system.…
Page 52: How will you use such sticks to answer the other two questions (Q2 and Q3)?
Page 52: How many numbers can you represent in this way using the sounds of the letters of your language?
Page 53: Do you see a way of extending this method to represent bigger numbers as well? How?
Page 54: Suppose you are using the number system that uses sticks to represent numbers, as in Method 1. Without using either…
Page 54: One way of extending the number system in Method 2 is by using strings with more than one letter — for example, we…
Page 54: Try making your own number system.
Page 56: Can you see how their number names are formed? Can you see how the names of the other numbers are formed?
Page 57: Quickly count the number of objects in each of the following boxes: two hens, a bunch of flowers, a row of five…
Page 57: What could be the difficulties with using a number system that counts only in groups of a single particular size?…
Page 59: So in Roman numerals, this number is MMCCCLXVII. Represent the following numbers in the Roman system.
Page 59: Example: Try adding the following numbers without converting them to Hindu numerals: (a) CCXXXII + CCCXIII Do it…
Page 60: How will you multiply two numbers given in Roman numerals, without converting them to Hindu numerals? Try to find…
Page 60: A group of indigenous people in a Pacific island use different sequences of number names to count different objects.…
Page 60: Consider the extension of the Gumulgal number system beyond 6 in the same way of counting by 2s. Come up with ways…
Page 61: Identify the features of the Hindu number system that make it efficient when compared to the Roman number system.
Page 62: Represent the following numbers in the Egyptian system: 10458, 1023, 2660, 784, 1111, 70707.
Page 62: What numbers do these numerals stand for?
Page 63: Express the number 143 in this new system.
Page 63: Write the following numbers in the base-5 system using the symbols: 15, 50, 137, 293, 651.
Page 63: Is there a number that cannot be represented in our base-5 system above? Why or why not?
Page 63: Compute the landmark numbers of a base-7 system. In general, what are the landmark numbers of a base-n system?
Page 64: Example: Add the following Egyptian numerals:
Page 65: Add the following Egyptian numerals:
Page 65: Add the following numerals that are in the base-5 system that we created:
Page 66: What is any landmark number multiplied by ∩ (that is, 10)? Find the following products —
Page 66: What is any landmark number multiplied by 100 (10²)? Find the following products —
Page 67: Find the following products — Thus, the product of any two landmark numbers is another landmark number! Does this…
Page 67: What can we conclude about the product of a number and ∩ (10), in the Egyptian system?
Page 68: Now find the following products — What would be a simple rule to multiply a number with ∩ (10)?
Page 69: To get an idea of how the abacus was used for calculations, let us consider a simple addition problem: 2907 + 43.…
Page 69: Can there be a number whose representation in Egyptian numerals has one of the symbols occurring 10 or more times?…
Page 70: Create your own number system of base 4, and represent numbers from 1 to 16.
Page 70: Give a simple rule to multiply a given number by 5 in the base-5 system that we created.
Page 71: Example: Let us represent the number 640 in this system. Grouping it into landmark numbers, we see that…
Page 73: Represent the following numbers in the Mesopotamian system —
Page 73: Look at the representation of 60. What will be the representation for 3,600?
Page 73: While writing the numerals, the spacing between symbols was not given the way we are giving it here. It was also…
Page 74: To address the issue arising out of blank spaces, the later Mesopotamians used a brilliant idea of assigning a…
Page 76: Represent the following numbers using the Mayan system:
Page 78: Where does the Hindu/Indian number system figure in the evolution of ideas of number representation? What are its…
Page 79: Hopefully, this gives you a sense of all the ideas that went into writing and computing with numbers in the way that…
Page 80: Why do you think the Chinese alternated between the Zong and Heng symbols? If only the Zong symbols were to be used,…
Page 80: Form a base-2 place value system using ‘ukasar’ and ‘urapon’ as the digits. Compare this system with that of the…
Page 80: Where in your daily lives, and in which professions, do the Hindu numerals, and 0, play an important role? How might…
Page 80: The ancient Indians likely used base 10 for the Hindu number system because humans have 10 fingers, and so we can…

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