1. Representing numbers in general form

Numbers form an integral part of our day-to-day lives. Objects surround us, and each of those requires a numerical representation in some form or the other.

 

We use numbers to count the objects, represent the distance between two objects, express their area and volume, etc.

 

Thus, numbers are everywhere.

 

We have learned about various numbers like whole numbers, negative numbers, natural numbers, and integers.

 

Now, let us learn to represent numbers in their general form.

Consider the two-digit number \(89\).

 

Recalling the concept of 'Place value in Numbers' from our lower classes, we know that \(89\) consists of \(8\) TENS and \(9\) ONES.

 

Therefore, \(89\) can also be represented as \((10 \times 8) + 9\).

 

From the example discussed previously, it is understood that two-digit numbers will be formed using some TENS and some ONES.

 

Let the some number of TENS be '\(a\)' and the some number of ONES be '\(b\)'.

 

Two-digit number '\(ab\)' can also be represented as \((10 \times a) + b\) or \(10a + b\).

Let us consider a three-digit number \(273\).

 

Similar to the construction of two-digit numbers, three-digit numbers are formed using HUNDREDS, TENS and ONES.

 

In this case, let HUNDREDS be represented as '\(a\)', TENS be represented as '\(b\)', and ONES be represented as '\(c\)'.

 

Therefore, the general form of the three-digit number '\(abc\)' is \((100 \times a) + (10 \times b) + c\) or \(100a + 10b + c\).

 

Therefore, \(273\) becomes \((100 \times 2) + (10 \times 7) + 3\).