6 Digit Numbers
6-digit numbers are natural numbers in which the first digit should be 1 or greater than 1 and the rest of the digits can be any number between 0 and 9. 6 digit numbers are mostly used to express larger quantities like the population of a state, or the price of cars. In this lesson, we will explore the world of numbers up to 6 digits. We will walk through the Indian and International numbering systems for the numbers up to 6-digits, see how to decompose them, clear misconceptions, and discover an interesting 6-digit number.
|1.||What are 6 Digit Numbers?|
|2.||How to Decompose 6-Digit Numbers?|
|3.||Common Mistakes or Misconceptions|
|4.||Place Value of 6 Digit Numbers|
|5.||FAQs on 6-digit Numbers|
What are 6 Digit Numbers?
In 6-digit numbers, the highest place value has a unique name in the Indian numeral system - a lakh. A lakh (1,00,000) is 1 followed by 5 zeros and it 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 the 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
Observe the Indian Place Value Chart given below which shows the place value up to ten arab.
There is no particular name for a lakh in the International system, and it is simply referred to as a hundred thousand. Let us have a look at the International Place Value Chart given below which shows the place values up to hundred million.
Commas in 6-Digit Numbers
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 are there in the number. For example, you would write 372672 as 3,72,672 to mean that the number has 3 lakhs, 72 thousand, 6 hundred, 7 tens, and 2 ones.
How to Decompose 6 Digit Numbers?
Decomposition of a 6-digit number means to write that number with the help of its place value and face value. Like we said at the start, a 6-digit number has place values up to a lakh. Given below are the names of the place values (starting from the right) in a 6-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 6-digit number like 2,31,273 (Indian System) and 231,273 (International System) and see how it gets decomposed.
|Digit 1 Place Value = 3 × 1||3|
|Digit 2 Place Value = 7 × 10||70|
|Digit 3 Place Value = 2 × 100||200|
|Digit 4 Place Value = 1 × 1000||1000|
|Digit 5 Place Value = 3 × 10000||30000|
|Digit 6 Place Value = 2 × 100000||200000|
Now, observe the decomposition of the same number as per the International Place Value Chart.
The Expanded form is useful to split and present the higher digit number in its units, tens, hundreds, thousands form. Decomposition of numbers leads to writing or reading of numbers in an expanded form which further helps to better understand and rightly read the higher digit numbers. The number 2,31,273 can be written in expanded form as 2,00,000 + 30,000 + 1,000 + 200 + 70 + 3.
The Significance of Zero in 6 Digit Numbers
Any zero which does not have any non-zero number to its left 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 6th number on the extreme left does not have any further non-zero number to its left. Additionally, in 002305, the 5th 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). On the other hand, with the addition of each zero to the right of any digit in the number, increase the value of that number, such as 238430 (which is a 6-digit number) becomes 2384300, which is a 7-digit number.
An Interesting 6-digit number
As you continue to explore your way around the exciting world of numbers, you will come across a number that 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 π. 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 = πD. 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 22/7, let us consider 1/7. This number 1/7 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
- 142857 × 2 = 285714
- 142857 × 3 = 428571
- 142857 × 4 = 571428
- 142857 × 5 = 714285
- 142857 × 6 = 857142
Common Mistakes or Misconceptions
Right from early grades, children face difficulties regarding the place value of digits in the given numbers and then they come across learning of the number system and conversions from one number system to another. Here children should build comfort writing the same number in both systems. Targeted practice helps. Given below are common mistakes and misconceptions.
Misconception: "One hundred thousand" and "one lakh" are two different numbers. 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.
Let us now understand how to write a 6-digit number in the Indian as well as the International System.
Place Value of 6 Digit Numbers
The best way to learn to write 6-digit numbers is to create a chart with all the place names listed. You must have observed that 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). Also, the given numbers can be represented in the standard form, words, or in the expanded form.
Tips and Tricks on 6 Digit Numbers
- Tip: Remember the zeros for two large numbers and all other larger or smaller numbers can then be written with reference to these two numbers.
"one crore" is 1 followed by 7 zeros.
"1 million" is 1 followed by 6 zeros.
- Trick: If we want to round off say 4,63,859 to the nearest thousand then underline all digits that are in the lower place values (ones, tens, and hundreds, in this example). Then replace those digits with zero, while doing this check the highest place value we are replacing (hundreds place i.e 8 in this example). If that is 5 or higher, increase the thousands place by one. So the rounded off number will become 4,64,000.
Important Points on 6 Digit Numbers
- 100 lakhs make a crore.
- The greatest 6-digit number is 9,99,999 which is read as nine lakh, ninety-nine thousand, nine hundred and ninety-nine.
- Interesting fact: On cheques, we write the amount in both ways (In digits as well as in words). Example: two lakh is written as Rs. 2,00,000 in the number space provided, and 'Rupees Two lakh only' is written as words in the line below.
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Examples on 6-Digit Numbers
Example 1: Arrange the numbers: 5, 7, 2, 3, 9, and 8, to find the greatest 6-digit number without repeating any digit, as per the Indian Place Value System.
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
Therefore, the greatest 6 digit number that can be formed using the given numbers is 9,87,532.
Example 2: How is the number 249132 indicated with commas and read in the Indian place value system and the International place value system?
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: 249,132. This is read as Two hundred forty-nine thousand, one hundred and thirty-two.
Example 3: Find the difference between the largest 6-digit number and the smallest 4-digit number and find its predecessor.
The largest 6-digit number is 9,99,999 and 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.
FAQs on Numbers Up to 6-digits
What is a 6-Digit Number?
A 6 digit number is a number that has 6 digits, where the first digit should be 1 or greater than 1 and the rest of the digits can be any number between 0-9. It starts from one lakh (1,00,000) and goes up to Nine lakh, ninety-nine thousand, nine hundred and ninety-nine (9,99,999).
How Many 6-Digit Numbers are there in all?
There are 9,00,000 six-digit numbers in all. This can be calculated using the following method.
- Step 1: Write the smallest 6 digit number, which is 1,00,000.
- Step 2: Then, write the largest 6 digit number, which is 9,99,999.
- Step 3: Find their difference and add 1 to it. This means 9,99,999 - 1,00,000 = 8,99,999 + 1 = 9,00,000
Therefore, there are nine lakh (9,00,000) 6-digit numbers in all.
How to Write 6 Digit Numbers in Words?
Let us take a 6-digit number 5,46,783. According to the Indian place value system, it is written as Five lakh, forty-six thousand, seven hundred and eighty-three.
What is the Smallest 6 Digit Number?
The smallest 6-digit number is 1,00,000.
What is the Largest 6 Digit Number?
The largest 6 digit number is 9,99,999.
What is the Sum of the Greatest and the Smallest 6-Digit Numbers?
The smallest 6-digit number is 1,00,000 and the greatest 6-digit number is 9,99,999. Thus, the sum of the greatest and the smallest 6-digit numbers is 1,00,000 + 9,99,999 = 10,99,999.
How do you Write a 6 Digit Number in the Expanded Form?
A 6-digit number can be written in the expanded form as per the place value of each of the digit in that number. For example, 6,78,912 = 6,00,000 + 70,000 + 8,000 + 900 + 10 + 2.
Do All 6 Digit Numbers have 6 Addends in their Expanded Form?
No, not all 6-digit numbers have 6 addends in their expanded form. For a 6-digit number, including zero as one of the digit, such as 5,60,981 will have 5 addends in its expanded form: 5,00,000 + 60,000 + 900 + 80 + 1. Thus, 6-digit numbers that have six different digits, not including zero, will have six addends in their expanded form.
Find the Largest 6 Digit Number Divisible by 16.
999984 is the largest 6-digit number which is divisible by 16. This can be calculated by using the following steps.
- Step 1: Write the largest 6-digit number which is 999999.
- Step 2: Divide 999999 by 16 and we get 62499 as the quotient and 15 as the remainder.
- Step 3: Subtract the remainder from 999999 and we get 999984. therefore, 999984 is the largest 6-digit number which is divisible by 16.
What is Least 6 Digit Number which is a Perfect Square?
100489 is the least 6 digit number which is a perfect square. This can be calculated by using the following steps.
- Step 1: Write the smallest 6-digit number which is 100000.
- Step 2: Find the square root of 10000 which is 316.23, so 100000 cannot be a perfect square.
- Step 3: Find the number nearest to 316.23 which is a square root. We will try 3172. We can see that 3172 = 100489. Therefore, the least 6 digit number which is a perfect square is 100489.