## Introduction to Numbers up to 9-Digits

Introduce 9-digit numbers via some anecdote. 3-4 lines max.

## The Big Idea: What are 9-digit numbers?

- Numbers which involve 10000000s place. Stress upon the concept of place value
- We have only ten unique symbols (0, 1, 2, … 8, and 9). Using just these ten unique symbols we can create as many numbers as we wish. The concept of place value allows us to do this.
- The digit 4 if in the rightmost position (ones place) has the value 4. But if we move it to the second position from the right (tens place) it’s value becomes 40. Move one more position and the digit 4 has value 400.
- Essentially think it terms of tiny pebbles. If we have ten of them… we trade them for a larger rock. 10 large rocks can in terms be traded with flintstone.
- So to show the number 123 we could show 123 pebbles, or 12 rocks + 3 pebbles or 1 flintstone + 2 rocks + 3 pebbles.
- Since we cannot use rocks or other new symbols, we denote this in numbers using placement of digits. Rightmost place is the lowest value. Every subsequent placement is 10 times more than the value to its right.
- The next para should be dedicated to showing the decomposition of the place values and how they come together to form a 9 digit number. (6-7 lines of text).
- Use visual aids and a geogebra widget to illustrate the concept.

## What are 9-Digit numbers? Why are they important?

This is when things get slightly complicated when it comes to pure numbers. Start this segment by elaborating the two different systems of representation, Indian and International. Explain to users that the difference is merely superficial and causes only a change in the nomenclature not the value.

Use Geogebra widget to illustrate the point (if possible). Or resort to use of the Abacus or any visual aid that helps users picture these large numbers as opposed to having to memorise them.

### Common doubts that arise:

Students usually struggle with both place and face value especially when it comes to representing the same number in the two different number systems. So write about the best possible way to alleviate that problem. (remember the answer is mostly visual) Use interactive widgets and or visual aids to help the reader get a better grasp of what you are trying to convey. (text should not exceed 6-7 lines).