You have landed on the right page to learn about 4-Digit Numbers. Counting things is easy for us now. We can count objects in large numbers, like the number of students in the school, and represent them through numerals. We can also communicate large numbers using proper number names. Thousands of years ago, people were only aware of small numbers. Then, gradually, they learned how to handle large numbers and how to express large numbers in symbols.

As human beings processed, there was a greater need for the development of mathematics; thus, it grew further and faster. This detailed article on 4-Digit Numbers would help students get a better understanding of the subject. Numbers are used in many different areas and in various ways. We will learn about the four-digit numbers to understand how it works. Continue reading to know more.

Define 4 Digit Numbers

Definition: A \(4\)-digit number is a number that contains four digits.

After \(999\), the first four-digit number begins with \(1000\). Then the following \(9000\) numbers we have are four-digit numbers. In the table shown below, each of the place values has a number, and so you can get a number with \(4\) digits.

Example: \(4536,\,8796,\,2983,\,9879\) are a few of the samples.

Decomposition of 4-Digit Number

1. Thousands
2. Hundreds
3. Tens and
4. Units

That is why the multiplier to be used for each of the digits of a \(4\)-digit number \(1000,100,10\) and \(1\) respectively. Let us examine the number \(2365.\)

To decompose the Number, we proceed as given below:

\(2365 = \,(2\, \times \,1000) + (3\,\, \times \,100)\, + 3(6\,\, \times \,10)\, + \,(5\,\, \times \,1)\,\)

\( = 2000\,\, + \,300\,\, + \,60\,\, + \,\,5\, = \,2365\)

Now, consider the number \(2365,2635,2563\) and \(3652\) and notice the value of the same digit \(3\) in each of these numbers.

\(2365\,\, \to \,\,3\) has hundreds’ place and a place value of \(300\)

\(2635\,\, \to \,\,3\) has tens place and a place value of \(30\)

\(2563\,\, \to \,\,3\) has units place and a place value of  \(3\)

\(3652\,\, \to \,\,3\) has thousands’ place and a place value of  \(300\)

This tells us that the value of a digit is not the only thing that determines its place value in a \(4\)-digit number.

Forming and Reading 4-Digit Numbers

The below-given block represents the number thousands: \(1000\)

The below-given block represents the number hundreds: \(100\)

The below-given block represents the number tens: \(10\)

The below-given block represents the number ones: \(1\)

By looking at the given blocks below, we can form a four-digit number.

Here, we can see \(3\) thousand \(2\) hundreds \(4\) tens \(8\) ones, and the number formed here is \(3248\) and this can be written in words as ‘Three thousand two hundred forty-eight’.

Example: Few more examples are given below:

1. \(4000\, + \,700\, + \,60\, + \,5\, = \,4765\,\, \to \) Four thousand seven hundred sixty-five.
2. \(9000\, + 800 + 60\, + 4\, = 9864\, \to \) Nine thousand eight hundred sixty-four.
3. \(7000\, + \,900 + 30 + 2\, = 7932\, \to \) Seven thousand nine hundred thirty-two.

Commas in 4-Digit Numbers

In all the \(4\) digit numbers, the \({4^{{\rm{th}}}}\)  digit, which is on the extreme left, represents the thousands place. It is the standard convention to apply a comma between the \({4^{{\rm{th}}}}\) and \({3^{{\rm{th}}}}\) digit, that is thousands places and hundreds.

So, while the \(3\)-digit number \(473\) is written simply as \(473\) however, the \(4\)digit number \(6784\) will be written as \(6,784\) by using the comma. We do not have any specific mathematical reason behind doing this.

The \(4\) digit number is longer than \(3\)-digit or \(2\)-digit number, and the use of the comma only helps us to make the number more readable.

Facts of 4-Digit Numbers

1.There are fascinating facts of the \(4\)-digit numbers, which are given below:

2. You have \(4\) numbers (any number from \(0 – 9\)) in a \(4\)-digit number.

3. You are aware of the smallest \(4\) digit number that is \(1000\) and the greatest \(4\) digit number is \(9999\).

4. After starting at \(1000\) the four-digit numbers end at \(9999\), so there are \(9000\)  four-digit numbers in total in between these two numbers and including them.

Solved Examples on 4-Digit Numbers

Q.1. Find the sum of the greatest four-digit number and the smallest \(4\) digit number.
Ans: We know that,
The greatest \(4\)-digit number is\(9999\)
The smallest \(4\)-digit number is \(1000\)
So, we need to add these two numbers.
Now, \(9999\, + \,1000\)
\( = \,10999\)
Hence, the required answer is \(10999\)

Q.2. Find the difference of the greatest four-digit number and the smallest \(4\)digit number.
Ans: We know that,
The greatest \(4\)-digit number is \(9999\)
The smallest \(4\)-digit number is \(1000\)
So, we need to subtract these two numbers.
Now, \(9999\, – \,1000\)
\( = 8999\)
Hence, the required answer is \(8999\)

Q.3. Write the expanded form of the number \( 8976\,\,and\,3482\)
Ans: Given, \(8976\) and \(3482\)
We need to write the expanded form of these two numbers.
So,\(8976\) we see that \(8\) is in the thousands place \(9\) is in the tens place,\(7\) is in the one’s place.
Now, \( = 8976\, = \,8000\, + \,900\, + \,70\, + 6\)
Similarly, \(3482\) in the number \(3\) is in the thousands place, \(4\) is in the hundreds place, \(8\) is in the tens place, \(2\) is in the ones place.
Thus, \(3482\, = \,3000\, + 400\, + 80\, + 2\)
Hence, the expanded form of \(8976\) is \(8000\, + \,900\, + \,70\, + 6\) and \(3482\) is \(3000 + 400 + 80 + 2\)

Q.4. Find the sum of \(6\) thousands, \(5\) hundred \(7\) tens and \(2\) ones and \(3\) thousands ,\(4\) hundred and \(1\) one. From the total, subtract \(1\) thousand, \(1\) hundred, \(1\) ten and \(1\). one
Ans: we know that,
\(6\) thousand, \(5\) hundred, \(7\) tens and \(2\) ones \( = \,6572\)
\(3\) thousand, \(4\) hundred, and \(1\) one \( = \,3401\)
\(1\) thousand, \(1\) hundred, \(1\) ten and \(1\) one \( = \,1111\)
Now, we will add them \(6572\, + \,3401\, = \,9973\)
Hence, the required answer is \(8862\)

Q.5. Compare the given numbers \(6789\) and \(6743\)
Ans: Given to compare \(6789\) and \(6743\)
When you want to compare any number, we start comparing from the left side from thousands places.
So, we can see that the digits in the thousands place and the hundreds place are the same.
Now, compare the tens place digits \(\to 8 > 4.\)
Here, you can clearly see that the number \(8\) is greater than the number \(4\).
This means \(6789\) is the greater number than the number \(6743\)
Hence, the required answer is \(6789\,\, > \,6743\).

Q.6. Write the given numbers in the words: \(7893,\,2365,\,9021\)
Ans: Given to write the given numbers in words: \(7893,\,2365,\,9021\)
So, we need to understand the place value of the given number and then write the number name.
We will write the numbers first in the place value table to understand

Thousands	Hundreds	Tens	Ones
\(7\)	\(8\)	\(9\)	\(3\)
\(2\)	\(3\)	\(6\)	\(5\)
\(9\)	\(0\)	\(2\)	\(1\)

Here, the number name of \(7893\) is Seven thousand eight hundred ninety-three.
The number name of \(2365\) is Two thousand three hundred sixty-five.
The number name of \(9021\) is Nine thousand twenty-one.
Hence, the required answer is given above.

Summary

In the given article, we have learnt about the \(4\) digit numbers, then discussed how to form the four-digit number and then read the same. We also had a glance at the facts of four-digit numbers like the number zero cannot be used in the thousands place, four digits are required to form the four-digit number, etc., then later the importance of the use of the commas. Understanding of the decomposing of the four-digit numbers is also given, which is very important. You have also gone through some solved examples along with a few of the FAQ.

Frequently Asked Questions

Q.1. What is the best 4-digit number?
Ans: The best \(4\)-digit  PIN is ‘\(8068\)’ -or it was until the researchers at Data Genetics told everyone. The researchers went through a set of \(3.4\) million four-digit personal identification numbers and found “\(8068\)” came up only \(25\) times.

Q.2. What is the hardest 4-digit code?
Ans: Among the \(10.000\) possible combinations of \(4\) digit codes, it is experienced that \(4\) digit code is the number \(3861\).

Q.3. What could be a 4-digit code?
Ans: There are \(10.000\) possible combinations that the digits from \(0 – 9\) can be used to arrange and form a four-digit code.

Q.4. How many 4-digit numbers are there?
Ans: Four-digit numbers are the numbers that have four digits in them, i.e. they have ones, tens, hundreds, and thousands place. You know that four-digit numbers start from the number \(1000\)and end at the number \(9999\) four-digit numbers.

Q.5. Explain 4-digit numbers along with examples.
Ans: When you multiply a unit with ten, you get a two-digit number. What happens when \(1000\)?
Each place values have a number, so you would get a number with \(4\) digits.

Q.6. How do you write 4–digit numbers?
Ans: There are four digits in a four-digit number. They are placed according to their values from right to left at ones, tens, hundreds, and thousands.

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