Decimals are the natural extension of the place value system to represent decimal fractions like $\frac{1}{10}$, $\frac{1}{100}$, $\frac{1}{1000}$, and so on, and their sums.
For example, the number $27.53$ refers to a quantity that has:
To divide any number by a number of the form 1 followed by zeroes (10, 100, 1000, etc.):
Examples: $24 \div 100 = 0.24$, $12 \div 1000 = 0.012$, $12345 \div 1000 = 12.345$.
Multiplication of decimals is conceptually the same as the multiplication of their corresponding fractions.
Example: To evaluate $5.96 \times 24.8$:
When we divide a decimal by 10, 100, 1000, etc., we move the decimal point to the left by as many places as there are zeroes in the divisor.
Example: $18.7 \div 100 = 0.187$, $0.13 \div 10 = 0.013$.
The procedure of division using place value can be extended to find quotients with decimal values by regrouping remainders into smaller place values (Ones to Tenths, Tenths to Hundredths, etc.).
Important Rule: When we regroup Ones into Tenths, we must place a decimal point in the quotient.
Example: $237 \div 8 = 29.625$
When the divisor is a decimal, we can convert it into a counting number by multiplying both the dividend and the divisor by a suitable power of 10 (10, 100, 1000, etc.).
Example: $$\frac{4.68}{0.13} = \frac{4.68 \times 100}{0.13 \times 100} = \frac{468}{13} = 36$$
Some decimal divisions never end because a non-zero remainder keeps repeating in a cycle.
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This calendar system keeps our calendar year aligned with the astronomical year with an error of only about 0.2 days every 1000 years.