This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions for the questions from the image: 1. Let's say the answers and write in the blanks as quickly as possible. a) The digits in Hindu-Arabic number system are \0, 1, 2, 3, 4, 5, 6, 7, 8, 9\ b) The face value, place and place value of 5 in 3517248 are The digit 5 is in the hundred thousands place. Face value: 5 Place: Hundred thousands Place value: 5 × 100,000 = 500,000 Answer: 5, Hundred thousands, 500,000 c) The place value of 9 in 46904317 is ...................., whereas, it is .................... in 49604317. In 46904317, the digit 9 is in the hundred thousands place. Its place value is 9 × 100,000 = 900,000. In 49604317, the digit 9 is in the millions place. Its place value is 9 × 1,000,000 = 9,000,000. Answer: 900,000, 9,000,000 d) If the expanded form of a numeral is 3 × 10^4 + 2 × 10^2, the numeral is .................... Step 1: Calculate the value of each term. 3 × 10^4 = 3 × 10,000 = 30,000 2 × 10^2 = 2 × 100 = 200 Step 2: Add the values. 30,000 + 200 = 30,200 Answer: 30,200 2. Let's say and write the answers as quickly as possible. a) The least natural number is Answer: 1 b) The least whole number is Answer: 0 c) The greatest whole number is Answer: Undefined (or does not exist) d) Between N = \1, 2, 3, ...\ and W = \0, 1, 2, 3, ...\, the universal set is The set of whole numbers W contains all elements of N and also 0. Therefore, W can serve as the universal set for N and W. Answer: W or \0, 1, 2, 3, ...\ e) The greatest number of 5-digits is Answer: 99999 f) The least number of 6-digits is Answer: 100000 g) The greatest number of 4-digits formed by 8, 3, 0, 6 is To form the greatest number, arrange the digits in descending order. Answer: 8630 h) The least number of 5-digits formed by 7, 0, 2, 4, 9 is To form the least number, arrange the digits in ascending order, ensuring the leading digit is not zero. Digits: 0, 2, 4, 7, 9. The smallest non-zero digit is 2. Answer: 20479 i) How many millions are there in 40 lakh? Step 1: Convert 40 lakh to standard form. 1 lakh = 100,000 40 lakh = 40 × 100,000 = 4,000,000 Step 2: Convert to millions. 1 million = 1,000,000 4,000,000 ÷ 1,000,000 = 4 Answer: 4 j) How many crores are there in 3 hundred million? Step 1: Convert 3 hundred million to standard form. 3 hundred million = 3 × 100,000,000 = 300,000,000 Step 2: Convert to crores. 1 crore = 10,000,000 300,000,000 ÷ 10,000,000 = 30 Answer: 30 3. Creative Section - A Write the place names of coloured digits in Nepali as well as in International numeration systems. Also write the face value and place value of the coloured digits. (Assuming the "coloured digits" are the first digit of each number, as they are not visible in the image.) a) 74809165 The assumed coloured digit is 7. Nepali (Indian) System: Number: 7,48,09,165 Place Name of 7: Crores Face Value of 7: 7 Place Value of 7: 7 × 1,00,00,000 = 7,00,00,000 International System: Number: 74,809,165 Place Name of 7: Ten Millions Face Value of 7: 7 Place Value of 7: 7 × 10,000,000 = 70,000,000 b) 41062598700 The assumed coloured digit is 4. Nepali (Indian) System: Number: 41,06,25,98,700 Place Name of 4: Ten Arab Face Value of 4: 4 Place Value of 4: 4 × 10,00,00,00,000 = 40,00,00,00,000 International System: Number: 41,062,598,700 Place Name of 4: Ten Billions Face Value of 4: 4 Place Value of 4: 4 × 10,000,000,000 = 40,000,000,000 Last free one today — make it count tomorrow, or type /upgrade for unlimited.