Facts about decimals

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While numbers play an extremely important role in our everyday life, decimals give more meaning and accuracy to them.
A very commonly used mathematical term, here are a few basic facts about decimals.

1. What is a decimal?
A number represented to its utmost precision comprising of its integer and fractional equivalent is called a decimal.
Example: 36.25, 56.789…..
The numbers present after the zero may either be terminating or infinite.

2. How are decimals represented?
The common representation of decimals is as follows: Whole number. Fraction. Decimals are thus representations of numbers up to the smallest equivalent amount. One decimal digit to the right of the decimal point is the tenths place, while one place to the right of a decimal point is the ones place.
For example, in 36.1, the digit after the decimal point may be represented in terms of its fraction equivalent as 1/10.

3. History of decimals.
As per sources, the history of decimals dates back to the olden days in regions like China and India. Egyptians are also known to have adopted decimals to their counting system. By 1500, decimals were accepted by almost all professional mathematicians and became an integral part of the counting system around the globe.

4. How are decimals different from whole numbers?
A whole number represents complete integers and any zero added to the right of the number adds to its value. A decimal however, is simply a part of a whole number present to the right of the decimal point following the whole number.
Example: 67.809. Here, 67 is the whole number and 809 the decimal part.

5. What are the different types of decimals?
The two major types of decimals are recurring and terminating decimals.
Recurring Decimals: Decimals that go on continuously without terminating are called recurring decimals. These may also be called non-terminating decimals.
Terminating decimals: Decimals that stop after a particular decimal place and have specific values are called terminating decimals.

6. Uses of decimals.
Decimals are very commonly used in everyday life. It helps estimate value of numbers to utmost precision that would otherwise be impossible. Price of products in the market are represented in the form of decimals. In science, decimal values are very often used in calculations.

7. Relation between fractions and decimals.
In general, decimals and fractions have a very close relationship with each other. Any fraction a/b may be represented in its equivalent decimals form as c.d.
Example: A fraction 5/100 may be represented in its decimal form as 0.05.

8. Approximation of decimals.
Approximation of a decimal to its nearest whole number and decimal value can be done as follows:
Consider a decimal 45.678
The whole number approximation of the above number would simply be 46 as 45.678 is greater than 45.5.
The approximation of the same number to two decimal places would be 45.69 as 45.678 is greater than 45.675.

9. The mathematics behind decimals.
Any digit present after a decimal point is represented as its tenths, hundreds and so on. The value to the right of the decimal point is a sum of these individual values.
Given any number 3.415, the decimal part .415 = 4/10 + 1/100 + 5/1000.

10. Addition and subtraction of decimals.
Addition and subtraction of decimals is carried out by first aligning the decimal points of the two numbers. The empty decimal places in either number is filled with zeros. This is then followed by the required operation of addition or subtraction.

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