Large Numbers Around Us — Question 5

5 × 1000 + 7 × 10 + 2 × 1 Figure it Out (Pages 6-7) For each number given below, write expressions for at least two different ways to obtain the number through button clicks. Think like Chitti and be creative. (а) 8300 (b) 40629 (c) 56354 (d) 66666 (e) 367813 Solution: (a) (i) (8 × 1000) + (3 × 100) = 8300 (ii) (83 × 100) = 8300 (b) (i) (4 × 10000) + (6 × 100) + (2 × 10) + (9 × 1) = 40629 (ii) (40 × 1000) + (6 × 100) + (29 × 1) = 40629 (c) (i) (5 × 10000) + (6 × 1000) + (3 × 100) + (54 × 1) = 56354 (ii) (56 × 1000) + (35 × 10) + (4 × 1) = 56354 (d) (i) (6 × 10000) + (6 × 1000) + (6 × 100) + (66 × 1) = 66666 (ii) (66 × 1000) + (66 × 10) + (6 × 1) = 66666 (e) (i) (3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100)+ (13 × 1) = 367813 (ii) (36 × 10000) + (7813 × 1) = 367813 NCERT In-Text Questions (Page 7) Creative Chitti has some questions for you- (a) You have to make exactly 30 button presses. What is the largest 3-digit number you can make? What is the smallest 3-digit number you can make? (b) 997 can be made using 25 clicks. Can you make 997 with a different number of clicks? Solution: (a) For the largest 3-digit number: Press the +100 button 9 times: 9 × 100 = 900 Add 10 more presses using the +10 button: 10 × 10 = 100 Add the remaining 11 presses using the +1 button: 11 × 1 = 11 Sum: 900 + 100 + 11 = 1011, but that’s a 4-digit number. Scale back by reducing the number of +10 presses to 8 and +1 presses to 13. Largest 3-digit number: 993 (9 × 100 + 8 × 10 + 13 × 1) For the smallest 3-digit number Press the +10 button 8 times: 8 × 10 = 80 Add 22 more presses using the +1 button: 22 × 1 = 22 Smallest 3-digit number: 102 (8 × 10 + 22 × 1) (b) 997 with 34 Clicks 9 × (+100) = 900 8 × (+10) = 80 17 × (+1) = 17 Create questions like these and challenge your classmates. Solution: Do it yourself. Systematic Sippy is a different kind of calculator. It has the following buttons: +1, +10, +100, +1000, +10000, +100000. It wants to be used as minimally as possible. How can we get the numbers (a) 5072, (b) 8300 using as few button clicks as possible? Find out which buttons should be clicked and how many times to get the desired numbers given in the table. The aim is to click as few buttons as possible. Here is one way to get the number 5072. This method uses 23 button clicks in total. Is there another way to get 5072 using fewer than 23 button clicks? Write the expression for the same. Solution: (a) 5 × (+1000) = 5000 (5 clicks) 7 × (+10) = 70 (7 clicks) 2 × (+1) = 2 (2 clicks) Total clicks: 5 + 7 + 2 = 14 clicks Expression: 5 × 1000 + 7 × 10 + 2 × 1 = 5072 (b) For 8300: 8 × (+1000) = 8000 For: 3 × (+100) = 300 Total = 8000 + 300 = 8300 Figure it Out (Page 7)