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Kinh Nghiệm về How many numbers of 5 digits can be formed with the digits 0 2 3 4 and 5 if the digits many repeat? 2022

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Nội dung chính

    What are Numbers up to 5-Digits?Smallest 5 Digit NumberGreatest 5 Digit NumberPlace Values of Digits in Numbers up to 5-DigitsHow to Decompose 5-Digit Numbers?Commas in 5-Digit NumbersHow Many 5-Digit Numbers Can Be Formed?Important Notes on Numbers up to 5-DigitsFAQs on Numbers up to 5-DigitsWhat are 5-Digit Numbers?How Many 5-Digit Numbers are there?How do you Read a 5-Digit Number?How do you Write 5-Digit Numbers in Words?What is the Smallest 5-Digit Number?What is the Largest 5-Digit Number?What is the Sum of the Greatest and the Smallest 5-Digit Numbers?Which is the Greatest 5 digit number which is a Perfect Square?What is the Successor of the Greatest 5 Digit Number?How many numbers of 5 digits can be formed with the digits 0 2 3 4 and 5 if the digits may repeat?How many 5 digit numbers can be formed using the digits 0 1,2 3 4 and 5 which are divisible by 5 without repetition of the digits?How many 5 digit even numbers can be formed from the digits 0 1,2 3 and 4 if repetition of digits is not allowed?How many number of 5 digits can be formed?

How many odd numbers of $5$ digits can be formed with the digits $0,2,3,4,5$ without repetition of any digit?

I noticed that the last number can be filled in $2$ ways and first place can be filled in $3$ ways. Consequently, 2nd 3rd and 4th places can be filled in $3$, $2$ and $1$
ways respectively. Is there any flaw in this reasoning? Please guide further.

asked Jul 13, 2022 5:14

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3

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$colorgreencheckmarkquad$ You are good to go.

We count ways to select from the two odd digits for the units, from the three other non-zero digits for ten-thousandth place, and how to arrange the three remaining digits in the remaining places.   Then we go forth and mulltiply.
$$2cdot 3cdot 3! ~=~ 36$$

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5 digit numbers are the integers on the number line that start from 10,000 and go up to 99,999. These numbers contain a total of 5 digits in their numeric form. Let us learn more about numbers up to 5 digits in this page.

1.
What are Numbers up to 5-Digits?
2.
Place Values of Digits in Numbers up to 5-Digits
3.
How to Decompose 5-Digit Numbers?
4.
Commas in 5-Digit Numbers
5.
How Many 5-Digit Numbers Can Be Formed?
6.
FAQs on Numbers up to 5-Digits

What are Numbers up to 5-Digits?

Five-digit numbers start from ten thousand and extend up to ninety-nine thousand nine hundred and ninety-nine. These numbers contain integers the places of ones, tens, hundreds, thousands, and ten thousands. Any positive integer can be placed these places, keeping in mind that 0 cannot be placed on
the ten thousands place. This is because if 0 is placed here it will become a 4-digit number, like, 04356 becomes 4356. The following figure shows how a random 5-digit number, 86953 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.

Smallest 5 Digit Number

The smallest 5-digit number is 10,000 because 5-digit numbers start from 10,000 and the number before 10,000 is 9999 which is a 4-digit number.

Greatest 5 Digit Number

The greatest 5-digit number is 99,999 because the number after 99,999 is 1,00,000 which becomes a 6-digit number.

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‘. The following figure shows
the place values of this 5-digit number.

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. Here, 0 is in Thousands place = 0 × 1000 = 0, and 3 is in Hundreds place = 3 × 100 = 300, 4 is in Tens place = 4 × 10 = 40, and 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:

    The place value of 2 becomes 2 × 1000 = 2000 (the earlier place value of 2 was 20000)The place value of 3 becomes 3 × 10000 = 30000 (the earlier place value of 3 was 300)The place value of 4 becomes 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 is just before the digit on the hundreds place, that is, 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 placed 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 thousand
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 thousand 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 the ten thousands place in a 5-digit number can never be 0.

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    Numbers Up to 2 DigitsNumbers Up to 3 DigitsNumbers Up to 4 DigitsNumbers Up to 6 DigitsNumbers Up to 7 DigitsNumbers Up to 8 DigitsNumbers Up to 9 DigitsNumbers Up to 10 DigitsNumber Systems

FAQs on Numbers up to 5-Digits

What are 5-Digit Numbers?

A 5-digit number is a number that has 5 digits, in which 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 ten thousand (10,000) and goes up to ninety-nine
thousand, nine hundred and ninety-nine (99,999).

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 right, 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 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.

Which is the Greatest 5 digit number which is a Perfect Square?

The greatest 5 digit number which is
a perfect square is 99856. This is the square of 316 which means 3162 = 99856.

What is the Successor of the Greatest 5 Digit Number?

The greatest 5 digit number is 99,999. The successor of 99,999 is 1,00,000 which is read as one lakh as per the Indian place value chart and is read as a hundred thousand
(100,000) as per in International place value chart.

How many numbers of 5 digits can be formed with the digits 0 2 3 4 and 5 if the digits may repeat?

The number of 5 digit numbers that can be formed in this case are 14406. When repetition is not allowed.

How many 5 digit numbers can be formed using the digits 0 1,2 3 4 and 5 which are divisible by 5 without repetition of the digits?

Answer : `=2xx5xx6xx6xx6=2160` ways. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

How many 5 digit even numbers can be formed from the digits 0 1,2 3 and 4 if repetition of digits is not allowed?

∴ the total number of arrangements = 120 + 96 + 96 = 312.

How many number of 5 digits can be formed?

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.
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