Question 4 - Figure it out - Page 80 - Chapter 3 Class 8 - A Story of Numbers (Ganita Prakash)

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Question 4 The ancient Indians likely used base 10 for the Hindu number system because humans have 10 fingers, and so we can use our fingers to count. But what if we had only 8 fingers? How would we be writing numbers then? What would the Hindu numerals look like if we were using base 8 instead? Base 5? Try writing the base-10 Hindu numeral 25 as base-8 and base-5 Hindu numerals, respectively. Can you write it in base-2?Why Base-10? We likely use Base-10 because we have 10 fingers. If we had 8 fingers: We would likely use a Base- 𝟖 (Octal) number system. Digits: 0, 1, 2, 3, 4, 5, 6, 7 Counting: After 7 , the next number would be " 10 " (which would represent the value 8) Writing the number 25 (decimal) in other bases: Decimal Number (Our System): 25 Drag to change the number Base 10 (Decimal - 10 Fingers) 105 15 2 5 Base 8 (Octal - 8 Fingers) 85 15 3 1 Base 5 (Quinary - 1 Hand) 255 5S 15 1 0 0 Base 2 (Binary - Computers) 165 85 45 25 15 1 1 0 0 1Base-10 (Decimal): Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 25 (Two 10s + Five 1s) Base-8 (Octal): Digits: 0, 1, 2, 3, 4, 5, 6, 7 We need to find how many 8s fit in 25. 3 × 8=24. Remainder is 1 . So, 3 groups of 8 and 1 unit. Numeral: 𝟑𝟏 Base-5 (Quinary): Digits: 0, 1, 2, 3, 4 We need to find how many 5s fit in 25. 5×5=25. But " 5 " isn't a digit in Base-5 (digits are 0-4). We move to the next place value (5^2=25). One 25 , zero 5 s , zero 1 s . Numeral: 100 Base-2 (Binary): Digits: 0, 1, 2, 3, 4, 5, 6, 7 We need powers of 2(1,2,4,8,16,32…). Largest power in 25 is 16 . (Remainder 9). Largest power in 9 is 8 . (Remainder 1). No 4s, No 2s. One 1. 16+8+0+0+1. Numeral: 11001