Counting things is now easier for us. We can count vast numbers of objects, such as the number of students in a school, and express them using numerals. We can also use correct number names to communicate enormous quantities. People were only aware of small numbers thousands of years ago.

Then, over time, they learned how to work with enormous numbers and express them in symbols. As human beings processed more information, there was a larger need for mathematics to evolve; as a result, it grew further and faster. Numbers are utilised in a variety of contexts and in a variety of ways. To understand how Three-digit Numbers function, we shall learn about them.

In this article, we have explained Three-digit Numbers: Definition, Diagram, Facts, Examples, etc. Continue reading to know more.

Three-digit Numbers Definition

Definition: A three-digit number will consist of any three digits among the \(10\) digits with or without repletion, the only restriction being, a three-digit number cannot begin with the digit \(0\). 

We know that the first three-digit number is \(100\) and the last three-digit is \(999\). You are aware that we have nine one-digit numbers. Together with the digit \(0\), the ten digits are \(0, 1, 2, 3, 4, 5, 6, 7, 8,\) and \(9\). 

Example: \(567, 392, 190, 900\) etc., are few three-digit numbers.

Place Value of Three-digit Numbers

We know that the place value represents the position of the digit in the number. Therefore, every three-digit number’s value can be found by seeing which place value each digit has. 

Example: Take the number \(782\).

You will understand the place value of each digit here. Let’s write in the place value table for better understanding.

Hundreds	Tens	Ones
\(×100\)	\(×10\)	\(×1\)
\(7\)	\(8\)	\(2\)

So, you will write it as \(7 \times 100 = 700,8 \times 10 = 80,2 \times 1 = 2 = 700 + 80 + 2 = 782.\)

Decomposing Three-digit Numbers

You have already seen that a three-digit number contains the following place values-

1. Hundreds
2. Tens and 
3. Units

That is why the multiplier to be used for each of the digits of a three-digit number is \(100, 10\) and \(1\). Let us try and examine the given number \(635\). To decompose the number follow as given below:

\(635 = \left( {6 \times 100} \right) + \left( {3 \times 10} \right) + \left( {5 \times 1} \right)\)
\( = 600 + 30 + 5 = 635\)

Significance of Zero in Three-digit Number

Zero is not written at the left-most position or at the hundredth’s place in a three-digit number. So here you will, how the number \(404\) different from \(044\) or even \(004\)? 

In the number \(044\), the values are \(0×100+4×10+4×1=0+40+4=44\) , this makes the number a two-digit number that is \(44\), and in the case of \(004\), it becomes a single-digit number \(4\). The digit zero does not contribute any value to the number in these two examples, so that the numbers can be expressed as \(44\) or \(4\).

Expanded Form of Three-digit Numbers

The expanded form of a three-digit number can be written in three different ways. You will see that in the example given.

Example: Take the number \(823\).

1. So, the first form is the number \(823\) can be written as \({\rm{823 = 8 \times hundred + 2 \times tens + 3 \times ones}}\).
2. Now, in a second way, the number can be written as \(823=8×100+2×10+3×1\).
3. And thirdly, the number can be written in expanded form as \(823=800+20+3\). 

Thus, writing the number in three different ways is not wrong. In fact it helps us understand the number component in the expanded form of a three-digit number.

Common Mistakes of Three-digit Numbers

You can see that some of the common mistakes are observed while writing or reading a three-digit number. However, these mistake in reading and interpreting a three-digit number is often understood as some other number. In reading, writing, and interpreting a three-digit number, a correct understanding of the place value of the digits is essential.

You can see below the three common mistakes usually made by children in writing three-digit numbers.

1. If you have zero in units or tens place, there are chances of misunderstanding the number. 

Example: When asked to read \(150\) and \(105\), you may be confused. However, the model of the numbers through Base-10 blocks can help in a better understanding of the place value.

2. While writing the number One hundred twenty-three, you may often write \(100\) first and then attach \(23\) to it, which turns to \(10023\). 

Fact: Here, the misconception may arise due to a lack of understanding of place values. Using the base-\(10\) blocks or abacus shows children that a digit has a different value based on its position.

3. If you have been asked to form the smallest three-digit number with zero in it, there are chances of children placing the zero in the left-most position. 

Fact: Which is wrong as you cannot have the number zero in hundreds place when you want to write a three-digit number. 

Example: Form the smallest three-digit number using the given digit \(4,9,0\). You have to form the number \(409\) instead of \(049\) as zero has no value, and it makes a two-digit number in this case.

Facts of Three-Digit Numbers

The interesting facts of the three-digit numbers are given below:

1. We know that the smallest three-digit number is \(100\), and the largest three-digit number is \(999\).

2. The smallest three-digit prime number is \(101\).

3. We have \(900\) three-digit numbers in between \(100\) and \(999\), and in that, we have \(450\) even numbers and \(450\) odd numbers.

4. The largest three-digit number, which has all the distinct digits in it, is \(987\).

5. \(102\) is the smallest three-digit number between \(100\) and \(200\) which has all unique digits.

Solved Example – Three-digit Numbers

Q.1. Find the sum of the most significant three-digit number and the smallest three-digit number.
Ans: We know that,
The greatest three-digit number is \(999\).
The smallest three-digit number is \(100\).
So, we need to add these two numbers.
Now, \(999+100\)
\(=1099\) 
Hence, the required answer is \(1099\).

Q.2. Write the expanded form of the numbers \(375\) and \(921\).
Ans: Given, \(375\) and \(921\)
We need to write the expanded form of these two numbers.
So, \(375=300+70+5\)
Similarly, \(921\) in the number \(9\) is in the hundreds place, \(2\) is in the tens place, \(1\) is in the ones place.
Thus, \(921=900+20+1\)
Hence, the expanded form of \(375\) is \(300+70+5\) and \(921\) is \(900+20+1\).

Q.3. Compare the given numbers \(346\) and \(519\).
Ans: Given to compare \(346\) and \(519\)
When you want to compare any number, we start comparing digits from the left side or from the hundred places.
Now, compare the hundreds place digits \( \to 3 < 5\).
Here, you can see that the number \(5\) is greater than the number \(3\).
This means \(519\) is the greater number than the number \(346\).
Hence, the required answer is \(346 < 519\).

Q.4. Write the given numbers in words: \(830, 154, 942, 789\).
Ans: We are given to write the given numbers in words \(830, 154, 942, 789\)
Here, the number name of \(830\) is Eight hundred thirty.
The number name of \(154\) is One hundred fifty-four.
The number name of \(942\) is Nine hundred forty-two.
The number name of \(789\) is Seven hundred eighty-nine.
Hence, the required answers are given above.

Q.5. Find the difference between the greatest three-digit number and the smallest three-digit number.
Ans: We know that, the greatest three-digit number is \(999\) and the smallest three-digit number is \(100\).
So, we need to subtract these two numbers.
Now, \(999-100\)
\(=899\) 
Hence, the required answer is \(899\).

Summary

In the given article, we have learned about the three-digit numbers and then discussed how to understand the three-digit value. We also glanced at the common mistake that can be made in three-digit numbers, then later the understanding of the decomposition of the three-digit numbers along with the significance of zero in three-digit numbers.

Then, we have discussed the expanding form of three-digit numbers. There are a few solved examples, along with a few of the FAQs.

Frequently Asked Questions

We have provided some frequently asked questions about three-digit numbers here:

Q.1. How do you write numbers with \(3\) digit numbers?
Ans: There are three-digits in a three-digit number. They are placed according to their value from right to left at ones, tens, and hundreds.

Q.2. What are three ways to write a \(3\) digit number?
Ans: The three different ways to write the three-digit number is given below:
Let’s take the number \(759\)
The first way is you write in expanded form like \(7\) hundreds \(+5\) tens \(+9\) ones
The second way is you write the same number in words like \(759→\) Seven hundred fifty-nine.
The third way is you write the number in numeral form or, say, standard format like \(759\).

Q.3. What is the greatest three-digit number?
Ans: The greatest three-digit number is \(999\), which comes just before the smallest four-digit number, \(1000\).

Q.4. How do you find a \(3\) digit number?
Ans: The number is formed by using the digits \(0, 1, 2, 3, 4, 5, 6, 7, 8, 9\). When you combine the digits, you form a number, so when you combine three-digits together, you get a three-digit number explaining their place value, like \(731\) in this \(7\) is in the hundreds place, \(3\) is in the tens place, and \(1\) is in ones place.

Q.5. Explain three-digit numbers with an example?
Ans: A three-digit number is any number that will consist of any three-digits among the ten digits \(0, 1, 2, 3, 4, 5, 6, 7, 8,\) and \(9\) with or without repletion, the only restriction being, a three-digit number cannot begin with the digit \(0\). 
Example: \(634, 875, 945\), … etc., are few three-digit numbers.

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We hope this detailed article on three-digit numbers helped you in your studies. If you have any doubts or queries on this topic, you can comment down below and we will be more than happy to help you.