NCERT MCQ Solutions for Class 8 Maths Ganita Prakash Chapter 3 A Story of Numbers

Reema’s father tells her, “Around 4000 years ago, there flourished a civilisation in a region called Mesopotamia, in the western part of Asia, containing a major part of the present-day Iraq and a few other neighbouring countries.
This is one of the ways they wrote their numbers!”

“Humans had the need to count even as early as the Stone Age”. They counted food, livestock, trades, and offerings, also tracking days for important events like new moons or season changes. 

“The structure of the modern oral and written numbers that we use today had its origin thousands of years ago in India”.
It further mentions that the digits 0–9 were developed in India about 2000 years ago. 

The chapter mentions the Bakhshali manuscript as the “first known instance of numbers being written using ten digits, including the digit 0 (which was then notated as a dot)”.

“Aryabhata (c. 499 CE) was the first mathematician to fully explain, and do elaborate scientific computations with the Indian system of 10 symbols”.

“The Indian number system was transmitted to the Arab world by around 800 CE”. It was popularized by Al-Khwarizmi’s book (c.825) and Al-Kindi’s work (c. 830).

“Because European scholars learned the Indian numerals from the Arab world, they called them ‘Arabic numerals’ to reflect their European perspective”.
This terminology has recently been corrected in many textbooks. 

“The most commonly used terminologies for the numbers we use today are ‘Hindu numerals’, ‘Indian numerals’, and the transitional ‘Hindu-Arabic numerals'”.
It notes “Hindu” refers to geography not religion. 

In Method 1 (using sticks), the chapter defines it: “This way of associating each cow with a stick, such that no two cows are associated or mapped to the same stick is called a one-to-one mapping”. 

“An obvious limitation of using only the letters of the English alphabet in this form is that it cannot be used to count collections having more than 26 objects”.

The chapter describes one of the oldest methods: “One of the oldest methods of number representation is by making notches—marks cut on a surface such as a bone or a wall of a cave. These marks are also called tally marks”. 

The chapter shows how Gumulgal number names are formed, stating, “The numbers are counted in 2s, using which the number names are formed: 3 = 2 + 1, 4 = 2 + 2, 5 = 2 + 2 + 1, 6 = 2 + 2 + 2”. 

 Its notes this cognitive limit: “Most humans find it difficult to count groups having 5 or more objects in a single glance”.
This limitation may have influenced grouping strategies in number systems.

The chapter states, “Instead of representing 50 as XXXXX, a new symbol is given to it: L”.
The table of Roman numerals further lists ‘L’ for 50.

“People using the Roman system made use of a calculating tool called the abacus to perform their arithmetic operations”.
This highlights the difficulty of direct computation with Roman numerals. 

“Number systems having landmark numbers in which the (a) first landmark number is 1, and (b) every next landmark number is obtained by multiplying the current landmark number by some fixed number n is said to be a base-n number system”. 

The chapter states, “The Egyptian number system is a base-10 system, and the number system that we created is a base-5 system”.
This aligns with its landmark numbers being powers of 10.

“If larger and larger numbers needed to be represented, then there was a need for inventing an unending sequence of symbols for higher and higher powers of 10”.

“In later times, it became a base-60 system, also called the sexagesimal system, with a very efficient number representation”.
This system’s influence is seen in time measurements.

The chapter defines it as, “Such a number system (having a base) that makes use of the position of each symbol in determining the landmark number that it is associated with is called a positional number system or a place value system”.