In this mini lesson, we will explore the world of numbers upto 6-digits. We will walk through the Indian and International numbering systems for the numbers upto 6-digits, see how to decompose them, clear misconceptions and discover an interesting 6-digit number.

Hey Friends! Can you write the population of the state where you live in number form? How about writing down the price of your favourite car in the number form as well?

When you buy a car or count a state's population you will look at six and seven digit numbers. This video introduces you to the world of one lakh.

We are excited to have you in the journey of 6-digit numbers. Let's get going!

 Lesson Plan

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In the 6-digit numbers, the highest place value is 1,00,000 which has a unique name in the Indian number system – a lakh.

A lakh is 1 followed by 5 zeros and is the smallest possible 6-digit number.

It is essential to understand the Indian numbering system at this stage because from the next higher place value (or next higher power of ten), the International numbering system would also be used, so the difference must be made clear.

There are three special numbers in the Indian numbering system – lakh, crore, and arab.

One lakh in numbers is written as 1,00,000 ; a crore is equal to a hundred lakhs and is expressed as 1,00,00,000

An arab is 100 crores and is expressed as 1,00,00,00,000

When we move to a greater number of digits in the following modules, we will also touch upon the International numbering system.

For now, it will suffice to understand that there is no particular name for a lakh in the International system, and it is simply referred to as a hundred thousand.

Commas in 6-Digit Numbers

Based on the details given above, you can understand that as per the Indian numbering system, there would be two commas used in any six digit number.

The first would demarcate the first three digits (from right) to show how many thousands there are, and the next would come after the first 5 digits from the right to show how many lakhs there are in the number.

For example, you would write 372672 as 3,72,672 to mean that the number has 3 lakhs, 72 thousands, 6 hundreds, 7 tens and 2 ones.

Let's proceed to learn how do we decompose a 6-digit number.

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Like we said at the start, a six digit number has place values up to a lakh.

These are the names of the place values (starting from the right) in a six digit number:

• Digit 1-Units
• Digit 2-Tens
• Digit 3-Hundreds
• Digit 4-Thousands
• Digit 5-Ten Thousands
• Digit 6-Lakhs

So let us take a random six digit number like 528497, and see how it gets decomposed.

Here PV stands Place Value,

Digit 1 PV = 7 × 1	7
Digit 2 PV = 9 × 10	90
Digit 3 PV = 4 × 100	400
Digit 4 PV = 8 × 1000	8000
Digit 5 PV = 2 × 10000	20000
Digit 6 PV = 5 × 100000	500000

Have a look at another 6-digit number 2,31,273 and observe carefully its decomposition.

The Significance of Zero in 6-Digit Numbers

Any zero which does not have any non-zero number to its right does not count in the digits of the 6-digit number.

Take, for example, two 6-digit numbers 023843 and 002305.

In both these numbers, the 6^th number on the extreme left does not have any further non zero number to its left.

Additionally, in 002305, the 5^th number from the right also does not have any further non zero number to its left.

So for 002305, the two numbers on the left extreme are without any value.

So the two numbers can actually be written as 23843 (which makes it a 5-digit number) and 2305 (which makes it a 4-digit number). 

We are sure the next section which deals with an interestind 6-digit number, will add to your understanding about these large numbers.

Want to know how a 5-digit number changes to a 6-digit number? The largest 5-digit number is 99,999

We are going to illustrate 99,999 through abacus and demonstrate how adding a bead at ones place brings changes in the place value of other beads.

See the transformation of 5-digit number to 6-digit number.

Sounds interesting? Press the Play button to begin.

Click RESET and PLAY in the simulation shown below to see it happen.

An interesting 6-digit number

As you continue to explore your way around the exciting world of numbers, you will come across a number which usually is written using 6 digits (although shorter versions are also used).

This number is called Pi (pronounced as Pie) and is represented as 3.14159 and the Greek letter \(\pi\).

It is defined as the ratio between a circle’s circumference and its diameter.

So, if the diameter is D, and circumference is C, then \(C = \pi D\).

In more simple terms, it is the ratio of the number 22 and the number 7

Although it is usually represented by six digits (and sometimes even smaller versions like 3.14 or 3.142), it is theoretically possible to have infinite digits in this number.

Now we come to the interesting part.

Instead of \(\begin{align}\frac{22}{7}\end{align}\), let us consider \(\begin{align}\frac{1}{7}\end{align}\)

This number \(\begin{align}\frac{1}{7}\end{align}\) is another cyclic number (it has infinite numbers after the decimal point), but we usually write it as 0.142857

Here are some amazing facts about 0.142857

• When you multiply these 6 digits 142857 by 7, you get 999999

• It is even more interesting to note that the same set of digits get repeated when you multiply 142857 by the numbers 1 through 6

• \(\begin{align}\!142857\! \times \!2 = \!285714\!\end{align}\)

• \(\begin{align}\!142857 \!\times \!3 = \!428571\!\end{align}\)

• \(\begin{align}\!142857 \!\times \!4 = \!571428\!\end{align}\)

• \(\begin{align}\!142857\! \times \!5 = \!714285\!\end{align}\)

• \(\begin{align}\!142857 \!\times\! 6 = \!857142\!\end{align}\)

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What are the Common Mistakes or Misconceptions?

• Misconception:  "One hundred thousand" and "one lakh" are two different numbers.
  
  In India, children are taught to name numbers based on both the Indian naming system and the International naming system.
  
  So, 100,000 is written as “One hundred thousand” as per the International naming system but “One lakh” as per the Indian system.

• Children tend to make mistakes when placing commas in numbers of 6 or more digits.
  
  This once again happens because of two conventions - the Indian system and the International system.
  
  Here children should build comfort writing the same number in both systems. Targeted practice helps.

Let's now understand how can we write a 6-digit number in Indian as well as International System.

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Create a Chart with All the Place Names Listed

Let children see how till ten-thousand the naming convention is the same.

But for 6 digits or higher the same number has two names.

The choice of names does not change the value of the number.

“One lakh” and “one hundred thousand” are equal (have the same value).

 

Let's get ready to solve some interesting questions based on what we have learnt so far. 

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Example 1

 

 

Using the Indian place value system, identify and write the number and its number name with the help of the shapes and blocks representing them.

Solution:

The number name of 4,23,869 is Four lakh, twenty three thousand, eight hundred and sixty nine.

The number is 4,23,869

Example 2

 

 

There are 6 balloons with numbers printed on them.

Arrange these numbers to find the greatest 6-digit number without repeating any digit.

Solution:

For the greatest number, the digit in the lakhs place will be the greatest: 9

Now the other numbers will be arranged in descending order: 9,87,532

The greatest number is 9,87,532

Example 3

 

 

How is the number 249132 indicated with commas and read in the Indian place value system and the International place value system?

Solution:

The Indian system separates these numbers by adding commas in this way: 2,49,132

This is read as Two lakh, forty nine thousand, one hundred and thirty two.

The International system separates these numbers by adding commas in this way: 2,49,132

This is read as Two hundred forty nine thousand, one hundred and thirty two.

Example 4

 

 

Find the difference between the largest 6-digit number and the smallest 4-digit number and find its predecessor.

Solution:

The largest 6-digit number is 9,99,999

The smallest 4-digit number is 1000

Their difference is: \(9,99,999\! -\! \!1000\! =\! 9,98,999\)

The predecessor of the difference is \(9,98,998\)

Example 5

 

 

Identify the two numbers shown in the abacus and calculate their sum.

Solution:

The number shown in the first abacus: 4,12,634

The number shown in the second abacus: 1,50,702

Their sum is: \(\ 4,12,634 + 1,50,702 \)=\( 5,63,336\)

The sum is 5,63,336

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 

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