explain decimal notation

Decimal notation is a system we use to represent numbers using digits 0 to 9. It is based on the decimal numeral system, also known as base-10. In this system, each digit's value is multiplied by powers of 10 based on its position in the number.

For example, consider the number 345. In decimal notation, the digit '3' represents 3 hundreds, the digit '4' represents 4 tens, and the digit '5' represents 5 ones. We can write this number as:

345 = (3 * 100) + (4 * 10) + (5 * 1)

Here, 100 represents 10^2 (10 raised to the power of 2), 10 represents 10^1, and 1 represents 10^0. The decimal point separates the whole number part (to the left) from the fractional part (to the right). The fractional part uses negative powers of 10. For example:

0.25 = (2 * 10^-1) + (5 * 10^-2)

The decimal point determines the place value of each digit. Digits to the left of the decimal point represent whole numbers, whereas digits to the right represent fractions or parts of a whole.

Decimal notation is widely used in everyday life, such as in money, measurements, and statistics, because it is easily understood and compatible with our base-10 counting system.