In this mini-lesson, we will explore the world of 5-digits numbers and their place values and common properties. We will learn how to write 5-digit numbers with commas and how they are formed. So what are we waiting for? Let’s begin!
In the video below, let us explore the concept of the Place Value of a 5-digit number with the help of an example.
It is interesting to play on an abacus, isn't it?
Let's watch this video and learn all about the place value for 5 digit numbers while playing this game.
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What Are Numbers up to 5-Digits?
When we talk about 5-digit numbers, we talk about the place values up to 10,000 which can be represented as:
Hit the play button in the simulation below and observe how adding 1 to the largest 4 digit number 9,999 forms a 5-digit number.
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.
Unlock the Mystical World of Numbers Up To 5-Digits!
You might be interested in reading these mini lessons for a better understanding of numbers up to 5-digits.
Explore them and deep dive into the mystical world of numbers up to 5-digits.
Click on a mini-lesson to explore further! |
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Numbers Up To 4-digits |
Numbers Up To 3-digits |
Indian Numeral System |
Place Value Chart |
What Are the Place Values of Digits in Numbers up to 5-Digits?
A Simple Idea: The Place Value of Numbers
As shown above, in a 5-digit number, every progressive place value is the earlier place value multiplied by 10
The number in the image above is 63,447 and is read as 'Sixty Three Thousands Four Hundred and Forty Seven'
Thus, we see that 5 digit numbers show the value of the range 10,000
The smallest five-digit number is 10,000 while the largest five-digit number is 99,999
These 90,000 possible 5-digit numbers can have any number from 0 to 9 in any of the places, except for the placement of zero such that there is no non-zero number to its left.
For example, 20340 is a five-digit number, but 02340 is actually a 4 digit number 2340
The number 37,159 in the image above is read as 'Thirty Seven Thousands One Hundred and Fifty Nine'
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
\(\begin{align}
& { \!2 \text { in Ten Thousand's place value }\!\!\! =\!\! 2\! \!\times\! \!10000 \!\!=\! \!20000\! } \\
& { \!0 \text { in Thousand's place value = } \!0 \!\!\times\!\! 1000 =\! 0 } \\
& { \!3 \text { in Hundred's place value } =\! 3 \!\!\times \!\!100 = \!300 } \\
& { \!4 \text { in Ten's place value } = \!4\!\! \times \!\!10 = 40 } \\
& { \!0 \text { in Unit's place value } =\! 0 \!\times\! 1 = 0 }
\end{align}\)
So the five digit number can be expressed in the following way:
\(\begin{align} { 20000 } \\ { + \quad\, 0 } \\ { + \,300 } \\ { + \;\;\,40 } \\ { + \quad \; 0 } \\ \hline 20340 \\ \hline \;\; \end{align}\)
How would the 5 place values change if we interchanged some of the digits?
Let us say we have the 5 digit number 32004
The change in place value of the same \(5\) digits:
- 2 would now have the place value of \(\begin{align} 2 \times 1000 = 2000 \end{align}\) (earlier place value of \(2\) was \(20000\))
- 3 would now have the place value of \(\begin{align} 3 \times 10000 = 30000 \end{align}\) (earlier place value of \(3\) was \(300\))
- 4 would have the place value of \(\begin{align} 4 \times 1 = 4 \end{align}\) (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 above numbers, all the zero digits have zero place value.
Generate a random 5-digit number in the simulation below and click on 'Expand the number' to see the place value of each digit in the number.
Let's play along!
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 hundred's 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 hundred's 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 thousand’s 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: \(\begin{align} 10 \times 10 \times 10 \times 10 \times 10 = 1,00,000\end{align}\)
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 thousand’s place).
When there is zero in the first place, the next position (Thousand's) can be filled up in ten ways, as can the Hundred's, Ten's and Unit's places.
So the number of 5-digit numbers that have zero as the first digit are:
\(\begin{align}10 \times 10 \times 10 \times 10 = 10,000\end{align}\)
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.
- 99,999 is the greatest 5-digit number.
- 10,000 is the smallest 5-digit number.
- The digit at ten thousand place in a 5-digit number can never be 0
Solved Examples
Example 1 |
Find the sum and difference of the greatest 5 digit number and the smallest 5 digit number.
Solution:
Greatest 5 digit number is 99,999
Smallest 5 digit number is 10,000
Their sum is \( 99,999 + 10,000 = 1,09,999 \)
Their difference is \(99,999 - 10,000 = 89,999 \)
\(\therefore\) Sum = 1,09,999 & Difference = 89,999 |
Example 2 |
What number does this represent?
Solution:
There are 4 counters in the Ten Thousand place.
There are 3 counters in the Thousands place.
There are 6 counters in the Hundreds place
There are 2 counters in the Tens place and 7 in the Units place.
Therefore, the number is \( 40,000 +3000+600 +20 +7 = 43,627\)
\(\therefore\) The number is 43,627 |
Example 3 |
Add the numbers represented by the rods and counters.
Solution:
On counting the number of counters in each place value, we see that:
Addend_{1} is 51,643 and Addend_{2} is 43,627
Their sum is \( 51,643 + 43,627 = 95,270\)
\(\therefore\) Sum = 95,270 |
Example 4 |
Write the number name and expanded form of 68,075
Solution:
We see that the number:
6 is in the Ten Thousand place
8 in the Thousands place
7 in Tens place
5 in Ones place
The number name is Sixty eight thousand seventy five.
The expanded form of the number is \(6\! \times\! 10,000 \!+ \!8\! \times\! 1,000\! +\! 0\!\! \times\! \!100\! +\!7\!\! \times\!\! 10\! +\!5\!\! \times\!\! 1\)
Example 5 |
Find the difference of the successor of the smallest 5 digit number and the predecessor of the largest 5 digit number.
Solution:
Successor of the smallest 5 digit number is \(10,000 + 1 = 10,001\)
Predecessor of the largest 5 digit number is \(99,999- 1 = 99,998 \)
Their difference is \(9,999 - 10,001 = 89,997 \)
\(\therefore\) The number is 89,997 |
- How many 5-digit numbers are odd numbers?
- I am a 5 digit even number and a multiple of 10.
My Ten thousands digit is half of the Hundreds digit and my Tens digit is double the Hundreds digit and I don't have any digit repeated. Who am i ?
Interactive Questions on Numbers Up To 5-digits
Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result
- There are 5 digits (any number from 0-9) in a 5-digit number.
- The Ten thousand place in a 5-digit number cannot be 0
- 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.
Let's Summarize
The mini-lesson was aimed at helping you learn about the numbers up to 5-digits. Hope you enjoyed learning about them and exploring the important properties and place values of digits in a number.
We would love to hear from you. Drop us your comments in the chat and we would be happy to help.
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Frequently Asked Questions(FAQs)
1. 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
2. How do you read a 5 digit number?
We read the 5 digit number from left to write from its Ten thousand place value to the units place.
Example: the number 21356 is read from left to right as 21,356
In number names, it is read as twenty-one thousand three hundred fifty-six.
3. How do you write 5 digit numbers in words?
We write the number name of a number from its ten thousands place to the units place.
Example: The number 31,256 is written as as thirty-one thousand two hundred fifty-six.