NCERT Solutions Ganita Prakash (Part 1) Chapter 1 .2 Land of Tens — Figure it Out

Book page 71 Updated on2026-09-05

Q1.

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.

Answer

Use each digit of the number as the number of presses of its own button.

Number	Expression with least clicks	Clicks
(a) 8300	(8 × 1000) + (3 × 100)	8 + 3 = 11
(b) 40629	(4 × 10000) + (0 × 1000) + (6 × 100) + (2 × 10) + (9 × 1)	4 + 0 + 6 + 2 + 9 = 21
(c) 56354	(5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1)	5 + 6 + 3 + 5 + 4 = 23
(d) 66666	(6 × 10000) + (6 × 1000) + (6 × 100) + (6 × 10) + (6 × 1)	6 × 5 = 30
(e) 367813	(3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100) + (1 × 10) + (3 × 1)	3 + 6 + 7 + 8 + 1 + 3 = 28

Why it happens: Any press count of 10 or more on a button can be replaced by one press of the next bigger button plus fewer small ones, saving 9 clicks. Keep doing this and every button ends up pressed 0 to 9 times — which is precisely the place value form of the number.

Q2.

Do you see any connection between each number and the corresponding smallest number of button clicks?

Answer

Yes — the smallest number of clicks is the sum of the digits of the number.

Number	Digit sum	Least clicks
8300	8 + 3 + 0 + 0 = 11	11
40629	4 + 0 + 6 + 2 + 9 = 21	21
56354	5 + 6 + 3 + 5 + 4 = 23	23
66666	6 + 6 + 6 + 6 + 6 = 30	30
367813	3 + 6 + 7 + 8 + 1 + 3 = 28	28

Why it happens: Each digit says how many of that place value the number contains, and each of those is exactly one button press. Add up all the digits and you have counted every press.

Try This: Which 5-digit number needs the most clicks? 99,999 — its digit sum is 45. Which needs the fewest? 10,000 — just 1 click.

Q3.

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.

Answer

Because place value notation is itself the “no waste” way of writing a number.

56354 = (5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1)
Digits: 5 | 6 | 3 | 5 | 4
Buttons: +10000, +1000, +100, +10, +1

Why it happens: Sippy's buttons are 1, 10, 100, 1000 … — exactly the place values of our number system. If any button were pressed 10 or more times, ten of those presses could be swapped for a single press of the next button, cutting 9 clicks. So the cheapest plan never presses a button more than 9 times, and a count from 0 to 9 for each place value is a digit. That makes the cheapest expression identical to the expanded form of the number.

Did you know? This is why our system is called a place value system — the position of a digit tells you which power of ten it is counting.

Was this helpful? Report an error