Land of Tens

In the Land of Tens, there are special calculators with special buttons.

1. The Thoughtful Thousands only has a +1000 button. How many times should it be pressed to show: (a) Three thousand? 3 times (b) 10,000? ____________
   (c) Fifty three thousand? ___________
   (d) 90,000? ______________ (e) One Lakh? ________________ (f) ____________? 153 times (g) How many thousands are required to make one lakh?

2. The Tedious Tens only has a +10 button. How many times should it be pressed to show: (a) Five hundred? _____________ (b) 780? _________ (c) 1000? _________ (d) 3700? ________ (e) 10,000? ___________ (f) One lakh? _____________ (g) ____________? 435 times

3. The Handy Hundreds only has a +100 button. How many times should it be pressed to show: (a) Four hundred? ___________times (b) 3,700? __________ (c) 10,000? __________ (d) Fifty three thousand? __________ (e) 90,000? __________ (f) 97,600? __________ (g) 1,00,000? __________ (h) _________? 582 times (i)
   How many hundreds are required to make ten thousand?
   (j)
   How many hundreds are required to make one lakh? (k) Handy Hundreds says, “There are some numbers which Tedious Tens and Thoughtful Thousands can’t show but I can.” Is this statement true? Think and explore.

4. Creative Chitti is a different kind of calculator. It has the following buttons: +1, +10, +100, +1000, +10000, +100000 and +1000000. It always has multiple ways of doing things. “How so?”, you might ask. To get the number 321, it presses +10 thirty two times and +1 once. Will it get 321? Alternatively, it can press +100 two times and +10 twelve times and +1 once.

5. Two of the many different ways to get 5072 are shown below: These two ways can be expressed as: (a) (50 × 100) + (7 × 10) + (2 × 1) = 5072 (b) (3×1000) + (20×100) + (72 ×1) = 5072

Find a different way to get 5072 and write an expression for the same.

Figure it Out

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. (a) 8300 (b) 40629 (c) 56354 (d) 66666 (e) 367813

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? Create questions like these and challenge your classmates.

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 less than 23 button clicks? Write the expression for the same.

Figure it Out

1. For the numbers in the previous exercise, find out how to get each number by making the smallest number of button clicks and write the expression.
2. Do you see any connection between each number and the corresponding smallest number of button clicks?
3. If you notice, the expressions for the least button clicks also give the Indian place value notation of the numbers. Think about why this is so.

What if we press the +10,00,000 button ten times? What number will come up? How many zeroes will it have? What should we call it? The number will be 100 lakhs, which is also called a crore. 1 crore is written as 1,00,00,000 — it is 1 followed by seven zeroes.