Land of Tens

Class 7 Maths · Chapter 1: Large Numbers Around Us · NCERT Ganita Prakash section 1.2

Learn

Imagine calculators with only one button each. A +1000 calculator needs 3 presses to show 3,000 and 100 presses to show one lakh. A +10 calculator needs 78 presses to show 780, and 10,000 presses for one lakh! A +100 calculator needs 1,000 presses for one lakh.

1,00,000 = 100 × 1,000 = 1,000 × 100 = 10,000 × 10

Now a calculator with many buttons: +1, +10, +100, +1000, +10000, +100000, +1000000. There are many ways to make a number. For 5,072: (5 × 1000) + (7 × 10) + (2 × 1), or (4 × 1000) + (10 × 100) + (7 × 10) + (2 × 1), or even (50 × 100) + (72 × 1).

5,072 = (5 × 1000) + (7 × 10) + (2 × 1)

Fewest clicks: to use as few clicks as possible, press each button only as many times as the digit in that place. For 5,072 that is 5 + 0 + 7 + 2 = 14 clicks. So the fewest clicks = the sum of the digits, and the way of pressing is exactly the number's place value form.

fewest clicks for 5,072 = 5 + 0 + 7 + 2 = 14

Why does this work? Ten presses of one button equal one press of the next button (10 × 100 = 1 × 1000). So whenever a button is pressed 10 or more times, we can swap ten of those presses for a single press of the next button and save 9 clicks. With no digit above 9 left, we have the fewest clicks.

Explore: which button presses are the fewest?

1. Tap the way that makes 5,072 with the fewest clicks.

Remember

• A number can be built from +1, +10, +100… presses in many ways.
• The fewest clicks = the sum of the digits, and it matches place value.

Quick check

A calculator has only a +100 button. How many presses show 53,000?

1. 530
2. 53
3. 5,300
4. 5,30,000

Think about it

With exactly 30 clicks of +1, +10 and +100, what is the largest 3-digit number you can make?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.