Numbers up to 5-Digits
Numbers up to 5-digits are the integers on the number line that start from 10,000 and extend up to 99,999. These numbers contain a total of 5 digits in their numeric form. However, there are a few properties and terms related to these numbers that we need to learn. Let us have a look at the article given here in order to understand these numbers better.
What Are Numbers up to 5-Digits?
These are the five-digit numbers that start from ten thousand and extend up to ninety-nine thousand nine hundred and ninety-nine. These numbers contain integers at the places of ones, tens, hundreds, thousands, and ten thousands. Any non-negative integer can be placed at any position except at ten thousand (zero can't be placed here). The given figure shows how a random 5-digit number is placed on an abacus. The place value of the five digits that make up the 5-digit number would be obtained by progressively multiplying the respective figure by 1, 10, 100, 1,000, and 10,000 starting from the rightmost digit and moving to the left.
The Place Values of Digits in Numbers up to 5-Digits
As shown above, in a 5-digit number, every progressive place value is the earlier place value multiplied by 10. For example, let us take a number: 37,159. This number can be represented in words, as, 'Thirty Seven Thousand One Hundred and Fifty-Nine'. We see that 5-digit numbers show the value of the range 10,000. Have a look at the figure given below to make the concept clear:
How to Decompose 5-Digit Numbers?
When we see a 5-digit number, the five digits will correspond to the 5 place values - Units, Tens, Hundreds, Thousands and Ten Thousands. Let us see how a 5-digit number can be decomposed into its place values. Let us continue with the same number 20340. 2 is in Ten Thousands place =2×10000=20000. 0 is in Thousands place = 0×1000=0. 3 is in Hundreds place =3×100=300. 4 is in Tens place =4×10=40. 0 is in Units place =0×1=0. Hence, the five-digit number can be expressed in the following way: 20000 + 0 + 300 + 40 + 0 = 20340.
Now, how would the 5 place values change if we interchanged some of the digits? Let us change the number 20,340 to another 5-digit number having the same numbers with interchanged digits, like, 32,004. The change in place value of the same 5 digits shows the following results:
- 2 would now have the place value of 2×1000=2000 (the earlier place value of 2 was 20000)
- 3 would now have the place value of 3×10000=30000 (the earlier place value of 3 was 300)
- 4 would have the place value of 4×1=4 (the earlier place value was 40)
- Zero is the only digit from 0 to 9 whose place value stays the same (zero) irrespective of its position.
In both the numbers given above, all the zero digits have zero place value.
Commas in 5-Digit Numbers
We saw the use of commas in four-digit numbers, and the position of the comma was to the left of the hundreds place. In a 5-digit number too, only one comma is to be used, and it is to be applied to the left of the hundreds place. For example, the 5-digit numbers 32958 and 20340 can be better expressed as 32,958 and 20,340 which helps in reading the numbers correctly.
How Many 5-Digit Numbers Can Be Formed?
As we said earlier, 02340 is not a five-digit number but a four-digit number 2340. A five-digit number cannot have 0 as the first digit on the left, which is the ten thousands place. Overall, every one of the 5 places of a 5-digit number can be filled up in ten ways, because it can have 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So each of the five places can be similarly filled up in ten ways. Therefore, the total number of combinations possible are 10×10×10×10×10=1,00,000.
Out of these 1,00,000 ways of forming a 5-digit number, we need to take out all the possibilities which have zero in the first position on the left (or the ten thousands place). When there is zero in the first place, the next position (Thousands) can be filled up in ten ways, as can the Hundreds, Tens, and Units places. So, the number of 5-digit numbers that have zero as the first digit are 10×10×10×10=10,000. If we subtract these 10,000 ways from the overall 1,00,000 ways, we are left with 90,000. Therefore, there are 90,000 unique 5-digit numbers possible.
Important Notes on Numbers up to 5-Digits
Here is a list of some important notes related to numbers up to 5 digits. These are helpful while we solve questions related to this topic.
- As the name says, a 5-digit number compulsorily has 5 digits in it.
- The smallest 5 digit number is 10,000 and the greatest 5 digit number is 99,999.
- There are 90,000 five-digit numbers in all.
- The digit at the ten thousands place in a 5-digit number can never be 0.
Example 1: Find the sum and difference of the greatest 5-digit number and the smallest 5-digit number.
The greatest 5-digit number is 99,999. The smallest 5-digit number is 10,000. Their sum is 99,999+10,000=1,09,999. Their difference is 99,999−10,000=89,999.
∴ Sum = 1,09,999 and Difference = 89,999.
Example 2: Write the number name and the expanded form of 68,075.
We see that the number 6 is in the Ten Thousands place, 8 is in the Thousands place, 0 is at the Hundreds place, 7 in the Tens place, and 5 in Ones place. The number name is Sixty-eight thousand seventy-five.
The expanded form of the number is (6 × 10,000) + (8 × 1,000) + (0 × 100) + (7 × 10) + (5 × 1). This can also be written as: 60,000 + 8,000 + 0 + 70 + 5 = 68,075.
FAQs on Numbers up to 5-Digits
How Many 5-Digit Numbers are there?
There are 90,000 five-digit numbers including the smallest five-digit number which is 10,000 and the largest five-digit number which is 99,999.
How do you Read a 5-Digit Number?
We read a 5 digit number from left to write, starting from the ten thousands place to the units place. For example, the number 21,356 is read from left to right, starting from 2, followed by 1, 3, 5 and then 6. In number names, it is read as twenty-one thousand, three hundred fifty-six.
How do you Write 5-Digit Numbers in Words?
We write the number name of a five-digit number just the way we read it. Starting from left to write, from the ten thousands place to the units place. For example, the number 31,279 is written as thirty-one thousand, two hundred seventy-nine.
What is the Smallest 5-Digit Number?
The smallest five-digit number is 10,000. It is read as ten thousand in number names.
What is the Fundamental Theorem of Algebra?
The fundamental theorem of algebra states that an algebraic expression of n degree has n roots. An algebraic expression of the form f(x) = xn has n roots as answers.
What is the Largest 5-Digit Number?
The largest five-digit number is 99,999 and it is written as ninety-nine thousand, nine hundred ninety-nine, in words.
What is the Sum of the Greatest and the Smallest 5-Digit Numbers?
The greatest 5-digit number is 99,999 and the smallest 5-digit number is 10,000. Their sum is 99,999 + 10,000=1,09,999.