Three digit numbers are from 100 to 999. We know that there are nine one-digit numbers, i.e., 1, 2, 3, 4, 5, 6, 7, 8 and 9. There are 90 two digit numbers i.e., from 10 to 99. One digit numbers are made by the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9. In making two digit numbers, zero (0) is also utilized along with digits 1 to 9. In two digit numbers one digit represents number of ones and the other represent the number of tens.

The digit representing ones is placed at one’s place while the digit representing ten’s is placed at ten’s place. As in 52, 5 is at ten’s place having its value 5 × 10 = 50 and 2 is at one’s place having it’s value 2 × 1 = 2.

Similarly, in 35, 5 is at one’s place having it’s value 5 × 1 = 5 and 3 is at ten’s place having its value 3 × 10 = 30 i.e., 35 = 30 + 5.

In the first ten two digits numbers the digits 0, 1, 2, …. are placed after 1 i.e., 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19. Then comes 2 at ten’s place. All the digits are placed after 2 i.e., 21, 22, 23, 24, 25, 26, 27, 28 and 29.

**The following table shows the formation of two digits numbers:**

Sophia has 99 beads. She uses 10 beads to make 1 garland. She has made 9 garlands and now she is left with 9 beads.

99 = 9 tens and 9 ones

She gets 1 more beads from her mother. She is now able to make another garland of 10 beads.

The total number of beads now 100.

99 and 1 more make 100

Ninety-nine and one more make one hundred.

After 99, the counting number is 100. This is a three digit number. When one is added to 99, the sum is 100.

In 100, there are 10 tens or 100 ones, i.e., (100 = 10 × 10 = 100 × 1). With the help of ones we get tens and with the help of ones and tens we make the numbers of two digits, i.e., from 10 to 99.

*We know that *

One ten = **ten** (10)

Two tens = **twenty** (20)

Three tens = **thirty** (30)

Four tens = **forty** (40)

Five tens = **fifty** (50)

Six tens = **sixty** (60)

Seven tens = **seventy** (70)

Eight tens = **eighty** (80)

Nine tens = **ninety** (90)

Ten tens = **one hundred** (100)

*Similarly, *

1 × hundred = **hundred** (100)

2 × hundred = **two hundred** (200)

3 × hundred = **three hundred** (300)

4 × hundred = **four hundred** (400)

5 × hundred = **five hundred** (500)

6 × hundred = **six hundred** (600)

7 × hundred = **seven hundred** (700)

8 × hundred = **eight hundred** (800)

9 × hundred = **nine hundred** (900)

10 × hundred = **ten hundred** (1000)

We see that the three digit numbers like 100, 200, 300, 400, 500, 600, 700, 800 and 900 are represented by the numerals having a digit and two zeros. This numbers are the multiples of two numbers i.e., 100 × 1, 110 × 2, 100 × 3, …….., etc.

But the three digit numbers are formed by placing the one and two digit numbers, i.e., from 1 to 99 after the fundamental digits 1, 2, 3, ….., 9 respectively as 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, ……., 117, 118, 119, ………, 125, 126, 127, …….., 134, 135, 136, ……….., 299, 300, 301, ….…., 400, ….…, 427, ………….etc.

In three digit numbers the digits are placed at one’s, ten’s and hundred’s place. At the extreme right of the number there is one’s place, then to the left of it there is ten’s place and to the left of it there is hundred’s place. The digits have their place value in a given number.

**For example****,** in 235 the place value of 5 is 5, of 3 is 30 and 2 is 200. We write this in words as *two hundred thirty five*.

Let us form the number 100 with the help of blocks. If we say one small block is 1 then a strip made of 10 small blocks will represent 10. A sheet made of 10 strips will show 100.

The three digits numbers may easily be explained with the help of mathematical apparatus called **ABACUS**.

Spike abacus has many iron spikes on a wooden base. The spikes may have globules having wholes. The spikes are named as ones, tens, hundreds, thousands etc. respectively from extreme right to the left.

The number of globules in the concerned spikes expresses the place value of the digit of the number.

In the given picture of the abacus, there are three spikes. In the first spike expressing ones, there are 2 globules, next to it there are 3 globules and in the third spike from the ones’ spike there are 4 globules.

2 globules of the one’s mark, spike express 2 × 1 = 2, 3 globules of the tens spike express 3 × 10 = 30 while 4 globule of the third spike i.e., hundreds spike express 4 × 100 = 400. Thus, the globules placed at different places represent the number 400 + 30 + 2 = 432.

Thus, with the help of ‘**abacus**’ we can understand the concept of three digit numbers.

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