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Numbers up to 10-Digits
A 10-digit number is a number that has 10 digits where the first digit must be any number between 1 to 9. The place value of the 10th digit is called a 'Billion' in the international place value system and an 'Arab' in the Indian number system. The smallest ten-digit number is written as 1 followed by 9 zeros, that is, 1000000000.
|1.||What are 10 Digit Numbers?|
|2.||How to Write Numbers up to 10-Digits?|
|3.||How to Decompose 10-Digit Numbers?|
|4.||FAQs on Numbers up to 10-Digits|
What are 10 Digit Numbers?
10-digit numbers are those numbers that start from 1000000000 and end on 9999999999. For example, 5,901,235,682 and 3,502,586,760 are 10-digit numbers.
How to Write Numbers up to 10-Digits?
A 10-digit number can be written in two ways, one is according to the International number system and the other is the Indian number system. The different placement of the commas in the two different number systems gives a 10-digit number two different names.
In the International number system, a 10-digit number is expressed by using commas just after every three digits from the right. The smallest 10-digit number is written as 1,000,000,000 and is called one billion. Since the third comma after the 9th digit from the right denotes the start of a billion, so this number is called 1 billion in the International number system.
In the Indian number system, the first comma comes after three digits from the right after the hundreds place value and the next comma comes after every two digits. In other words, the Indian Place Value System of numbers follows the 3:2:2 system of placing commas, so the smallest 10 digit number is written as 1,00,00,00,000. Since the third comma after the 7th digit from the right denotes the start of a crore, so this number is called 100 crores or one Arab in the Indian number system.
Comparison of the Indian System and the International System
Observe the following charts that show the numbers up to 10 digits according to the Indian Place Value Chart and the International Place Value Chart.
How to Decompose 10-Digit Numbers?
Any 10-digit number has place values up to one Billion or Arab.
These are the names of the place values (starting from the right) in a 10-digit number:
- Digit 1 – Units/Ones
- Digit 2 – Tens
- Digit 3 – Hundreds
- Digit 4 – Thousands
- Digit 5 – Ten Thousand
- Digit 6 – Lakhs
- Digit 7 – Ten Lakhs / Million
- Digit 8 – Crores / Ten Million
- Digit 9 – Ten Crores / Hundred Million
- Digit 10 – One Arab (Hundred Crores) / Billion
So, let us take a random 10-digit number - 5448626840, and see how it gets decomposed.
Here, PV stands for Place Value:
- Digit 1: PV = 0 × 1 = 0
- Digit 2: PV = 4 × 10 = 40
- Digit 3: PV = 8 × 100 = 800
- Digit 4: PV = 6 × 1000 = 6000
- Digit 5: PV = 2 × 10000 = 20000
- Digit 6: PV = 6 × 100000 = 600000
- Digit 7: PV = 8 × 1000000 = 8000000
- Digit 8: PV = 4 × 10000000 = 40000000
- Digit 9: PV = 4 × 100000000 = 400000000
- Digit 10: PV = 5 × 1000000000 = 5000000000
- Observe the different ways of placing commas in the number 5000000000: International Place Value System: 5,000,000,000; Indian Place Value System: 5,00,00,00,000
- Observe the different names of numbers according to the Indian Number System and the International Number System given below:
- One Lakh is equal to One Hundred Thousand
- Ten Lakh is equal to One Million
- One Crore is equal to Ten Million
- Ten Crore is equal to Hundred Million
- One Arab (Hundred crores) is equal to One Billion
Largest 10 Digit Number
The largest 10-digit number is 9,999,999,999 because the number that follows it is 10,000,000,000 which is an eleven-digit number.
Smallest 10 Digit Number
The smallest 10-digit number is 1,000,000,000 because its preceding number is 999,999,999 which is a nine-digit number.
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Numbers up to 10-Digits Examples
Example 1: Write the predecessor of the given 10-digit number 3,457,542,009.
The predecessor of 3,457,542,009 is 3,457,542,008.
Example 2: How is the number 6754349132 indicated with commas in the Indian place value system and the International place value system.
The Indian place value system represents this number by adding commas in the following way: 6,75,43,49,132.
The International place value system represents this number by adding commas in the following way: 6,754,349,132.
Example 3: Find the difference between the largest 10-digit number and the smallest 10-digit number.
The largest 10-digit number is 9,999,999,999
The smallest 10-digit number is 1,000,000,000
Their difference is 9,999,999,999 - 1,000,000,000 = 8,999,999,999
Practice Questions on Numbers up to 10-Digits
FAQs on Numbers up to 10-Digits
What is a 10-Digit Number?
A 10-digit number consists of 10 digits in which the first digit cannot be 0, it can be 1 or any number greater than 1. This is because if the first digit is zero it will become a nine-digit number. The remaining 9 digits can have any number between 0 to 9. For example, 1,592,654,012 is a ten-digit number.
Is a 10-digit Number called a Billion?
Yes, a 10-digit number in the international place value system is called a billion, because the place name of the 10th digit from the right is called a billion. For example, 3,000,000,000 is read as three billion.
What is the Largest 10-Digit Number?
The largest 10 digit number is 9,999,999,999. In words, we read this number as nine billion, nine hundred ninety-nine million, nine hundred ninety-nine thousand, nine hundred ninety-nine. The number that comes after 9,999,999,999 is 10,000,000,000 which is an 11 digit number, therefore, the largest ten-digit number is 9,999,999,999.
What is the Smallest 10-Digit Number?
The smallest 10-digit number has 9 zeros and the starting digit is 1. This number is called one billion and in figures, it is written as 1,000,000,000.
How Many Commas are there in a 10-Digit Number According to the International System?
According to the international number system there are three commas in a billion and it is written as 1,000,000,000.
How to write a 10 Digit Number in the Indian System?
According to the Indian place value chart, a ten-digit number, for example, 9753109826 can be written as 9,75,31,09,826 where the commas placed using the method of 2:2:3