How Many 3-Digit Numbers Are There In All?

There are 900 total 3-digit numbers available.

Three-digit numbers begin at 100 and go up to 999. Therefore, 100 is the smallest and 999 is the greatest three-digit number. The digit count in a number determines what kind of number it is in mathematics. A three-digit number will be described by the place values of all the digits present in it. Three-digit integers are made up of single digits, double digits, and zeros.

Let us count the numbers from 100 to 999.

From 101-200, there are 100 numbers.

Following the same pattern,

201-300 - 100 numbers

301-400 - 100 numbers

401-500 - 100 numbers

501-600 - 100 numbers

601-700 - 100 numbers

701-800 - 100 numbers

801-900 - 100 numbers

901-1000 - 100 numbers

There are 900 numbers, which includes 1000, which is a four-digit number, 900-1=899. We have yet to include the three-digit number 100, so 899+1=900.

Therefore, there are 900 three-digit numbers.

Place Value Of The Three-Digit Number

The place value of each digit in a three-digit number can be used to determine the value of each number. Let's consider the number 987. Since the first number is supposed to be in the unit's place and be in the rightmost position, it will be multiplied by 1. Consequently, its place value is 7. The second number is then 8, which is multiplied by ten because it is at the tens place. Thus, its place value is 8 x 10 = 80. The third number is located in the hundreds position. 9 is multiplied by 100, giving its place value as 9x 100 = 900. And the sum is, therefore, 900 + 80 + 7= 987.

No three-digit number can begin with 0. Two zeroes can also be present in a three-digit number, but they must be in the tens and units place, for example, 100, 200, 300, and 400. It should be noticed that the hundreds location cannot have zeros because the number would then become two digits. 067, for instance, becomes 67.

Arithmetic Progression approach to find number of 3 digit numbers

The last three-digit number is 999, which is our nth term of the Arithmetic progression. The first term is 100, which is a. Common difference is 1, which is d. We substitute the values to get the n in the Tn formula, which is given below,

Tn=a+(n−1)d

999=100+(n-1)1

999-100=n-1

899=n-1

n=899+1

n=900

Therefore, 999 is the 900th term, which signifies the number of terms is 900. So the total 3 Digit Numbers are 900.

Examples-

What is the largest and smallest three-digit number?

The largest three-digit number is 999, and 100 is the smallest three-digit number.

Which among the following is the three-digit number?

100,987, 067, 98, 563.

The three-digit numbers are 100, 987, and 563.