Numbers up to 3-Digit
The numbers are broadly classified based on the number of digits. Here, we shall look at the 3-digit numbers, their formation, and the importance of numbers and place values. The digits used to form higher digit numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The place value of a 3-digit number helps in understanding the value of each of the digits. The smallest of 3-digit numbers is 100 and the largest number is 999.
Learning 3-digit numbers is the building block for higher-digit numbers. Here we shall explore more about the importance, formation, and place value of numbers in numbers up to 3-digit numbers.
|1.||Place Value of 3-Digit Numbers|
|2.||Expanded Form of 3-Digit Numbers|
|3.||Common Mistakes of Numbers up to 3-Digits|
|4.||Operations of Numbers up to 3-Digits|
|5.||FAQs on Numbers up to 3-Digits|
Place Value of 3-Digit Numbers
Every three-digit number’s value can be found by seeing which place value each digit has. Let us consider the number 243. The first digit at the rightmost position is said to be at units place, so they would be multiplied by 1. Hence the product is 3 × 1 = 3. Then the second number is 4, and because it is at tens place, it is multiplied by 10. The value, therefore, is 4 × 10 = 40. The third number 2 is at the hundreds place. So 2 is multiplied by 100 and its value is 2 × 100 = 200. Therefore the number is 200 + 40 + 3 = 243.
Decomposing a 3-digit number: In a three-digit number, there are three place values used – hundred’s, ten’s, and units. Let us take one example to understand it better. Here, 465 is a three-digit number and it is decomposed in the form of a sum of three numbers. As 5 is at the unit's place, 60 is at the tens place and 400 is on the hundreds place.
Significance of Zero in 3-digit numbers: The number zero does not make any contribution to a 3-digit number if it is placed in a position where there are no other non-zero numbers to its left. So how is 303 different from 033 or even 003? In 033, the values are 0 × 100 + 3 × 10 + 3 × 1 = 0 + 30 + 3= 33 which means that the number actually becomes a 2 digit number i.e. 33, or in the case of 003, it becomes a single-digit number i.e. 3. In these two examples, the digits zero do not contribute any value to the number, so the numbers can be expressed as 33 or 3 as well.
Expanded Form of 3-Digit Numbers
The expanded form of a 3-digit number can be expressed and written in three different ways. Consider a three-digit number 457. The number 457 can be written in one form as 457 = 4 × hundreds + 5 × tens + 7 × ones. In the second way, the number 457 can be written as 457 = 4 × 100 + 5 × 10 + 7 × 1. And finally the number 457 can be expanded in the form as 457 = 400 + 50 + 7. All the three ways of writing numbers in the expanded form are correct. Writing a 3-digit number in the expanded form helps to know the constituents of the number.
Basically splitting or expanding a 3-digit number helps us to understand more about the 3-digit number. By splitting we know the number of hundred's, ten's, and units available in the 3-digit number.
Let us look at some of the below mentioned important points relating to 3-digit numbers. These help in a better understanding of 3-digit numbers.
- 100 is the smallest 3-digit number and 999 is the greatest 3-digit number.
- A 3-digit number cannot start with 0.
- 10 tens make 1 hundred which is the smallest 3-digit number and 10 hundred make a thousand which is the smallest 4-digit number.
- A 3-digit number can also have two zero's. The two zero's should be in the ten's place and the unit's place. Some of the examples of 3 digit numbers is 100, 200, 300, 400. The only necessary condition is that the zero's cannot be in the hundredth place.
Common Mistakes of Numbers up to 3-Digits
Some of the common mistakes are observed while writing or reading a 3-digit number. These mistake in reading and interpreting a 3-digit number is often understood as some other number. In the process of reading, writing, and interpreting a 3-digit number, the place value of the digits should be rightly interpreted. Here we have listed below the three common mistakes often committed by children in writing three-digit numbers.
- Misconception 1: Children make mistakes identifying numbers when there is a zero in the unit’s place or tens place. Example: When asked to read 130 and 103, students may get confused. It helps them to model the numbers through Base-10 blocks. That way they can see the ten’s and one’s place value explicitly.
- Misconception 2: When asked to write “one hundred twenty-three," students often write 100 first and then attach 23 to it thus ending up with the number “10023” Fact: This misconception arises due to a superficial understanding of place values. Using the base-10 blocks or abacus show children that a digit has different values based on its position.
- Misconception 3: Sometimes when asked to form the smallest 3-digit number given three digits that include zero, children place the zero in the left-most position. Fact: This is incorrect. Zero cannot be in the hundreds place if we are creating a 3-digit number. For example: the smallest 3-digit number using all digits of 5, 0, and 7 is 507 and not 057
Operations of Numbers up to 3-Digits
The four arithmetic operations of addition, subtraction, multiplication, and division can be conveniently performed across 3-digit numbers. In the process of performing these arithmetic operations, the place value of the corresponding number should be rightly matched. An error in matching the place value could result in wrong answers. Here we shall look at a simple activity using 3 digit numbers, to help us understand the changing pattern in each of the digits of the hundredth place, ten's place, and unit's place. This activity shall help in a better understanding of the learning needed for the 3 digit numbers.
Get students to skip count by 10 and 100 to build fluency with 3-digit numbers. First, start at 100. Then start from any random 3-digit number like 136.
Help children spot the pattern that when skip counting by 10, the digit in the ones place value does not change. Similarly, when skip counting by 100, the digits in the ones place and tens place does not change.
Use a 100-square grid to build fluency. Let students spot the pattern that moving one row up or down is the same as skip counting by 10. Moving columns (left or right) increases or decreases numbers by 1.
Often children are given three digits and asked to find the largest and smallest number three-digit number using all digits. The trick here is to arrange all digits in descending order to find the largest number.
To find the smallest number, arrange all digits in ascending order. But keep in mind that if zero is one of the digits, it cannot be placed to the left. E.g. Using the digits 7, 3, and 6, the largest number is 763 (digits in descending order) and the smallest number is 367 (digits in ascending order). Using the digits 4, 0, and 8, the largest number will be 840 but the smallest 3-digit number is 408 and not 048.
Example 1: How many 3-digit numbers are there?
For a 3-digit number, the hundreds place cannot be 0. It can be any other digit from 1-9. Hence, there can be 9 digits in the hundreds place. In the tens place and the one's place, there can be any digit from 0-9. There is a possibility of 10 digits in the hundredth place and 10 digits in the unit's place. Thus, there are 9 × 10 × 10 = 900 three-digit numbers in all. Therefore there are 900 three-digit numbers in all.
Example 2: A teacher wrote a puzzle on the board. "Add the smallest 2 digit number to the smallest 1 digit number. Subtract the sum from one less than the greatest 3 digit number". Emma said that the answer was 987. Rony said that it was 997. Who was right?
Smallest 2 digit number = 10. Smallest 1 digit number = 1. Sum of these two numbers = 11. One less than the greatest 3 digit number is 998. Subtracting 11 from 998, we get. 998 - 11 = 987. Therefore Emma's answer is correct.
FAQs on Numbers up to 3-digits
How Many 3-Digit Numbers are There?
There are a total of 900 three-digit numbers. These include the smallest 3 digit number - 100 to the largest 3 digit number - 999. The numbers beyond these 3-digit numbers are the 4-digit numbers, and the numbers less than the 3-digit numbers are the 2-digit numbers.
Which is the Largest 3 Digit Number?
The largest 3-digit number is 999. Adding 1 more to it will make it a 4-digit number.
What is the Sum of the Three Largest 3 Digit Numbers?
The three largest 3-digit numbers are 997, 998, 999. Their sum is 2994 as 997 +998 +999 = 2994.
How do you Teach a 3-Digit Number?
The 3-digit numbers can be first taught by understanding the place value of the digits. Further, we need to know the limitations of using numbers in each of the place values. In a 3-digit number, the number zero cannot be placed at hundred places.
What is the Smallest 3-Digit Number?
The number 100 is the smallest 3-digit number. Subtracting 1 from it makes it a 2-digit number. There are a total of 900 3-digit numbers, of which the number 100 is the smallest 3-digit number.
How do you Sum the 3-Digit Numbers?
The sum of 3-digit numbers is the same as the sum of 2-digit or higher-digit numbers. The only condition is that the sum of the digits in a particular place is carried over to the next place. The sum of the digits of units place is carried over to the ten's place, and the sum of the digits of the ten's place is carried over to the hundredth place.
How Many Even 3-Digit Numbers are there?
There are a total of 900 3-digit numbers. Of these half of them are even numbers and the remaining half are odd numbers. Hence there are 900/2 = 450 even 3- digit numbers.
Can a 3-Digit Number have Two Zeroes?
A 3-digit number can also have two zero's. The two zero's should be in the ten's place and the unit's place. Some of the examples of 3 digit numbers are 100, 200, 300, 400. The only necessary condition is that the zeroes cannot be in the hundredth place.