Concept of Decimals

Decimal is the part of algebra and is also a part of the standard system for denoting non-integer and integer numbers. In a decimal system, a whole number part and the fractional part are separated by using a dot known as a decimal point. Decimals can also be used instead of fractions because of their many advantages.

Decimal fractions can be used for different operations such as:

• Additio and subtraction

For subtracting and adding decimal fractions, the numbers that are before the decimal point should be placed in one column, whereas, the decimal point should be inserted into a column and subtracted and added regularly.

For example, 0.026+2.012

   0.026

+ 2.012

–––––––

   2.038

• Decimal fractions can be multiplied 

The decimal fractions can be multiplied by the powers of 10 which will shift the decimal point to the right as many places 10s are multiplied. 

For example, 5.6986 × 1000 = 5698.6

• Division of decimal fractions 

Decimal fractions can be divided by counting numbers. The number should be divided without the decimal point and once we get the quotient, the decimal point is added in as many places of the decimals as there were in the dividend. 

For example 0.0204÷17

should be divided normally: 204÷17=12

Now, 0.0204÷17= 0.0012.

How to use the decimal system?

To write the decimals one should place the whole number part on the left side of the decimal point whereas the fractional part on the right side of the decimal point. Here is an example of the decimal place value chart:

As we move from left to right, the place value digits get divided by 10. Therefore, a decimal value would determine the place value in tenths, hundredths, and thousandths. 

How can fractional parts be converted into decimals?

When a fraction is converted into decimal, the number that is represented in the form of p/q (p and q here are whole numbers and q is not equal to 0) by converting ‘q'(the denominator) to a power of 10. It can also be converted by a long division method.

The conversion of fractional parts into decimals is very easy and here is an example of how it can be done:

Long division method:

In this form of conversion, the long division method is used until we get zero as a remainder, or in the place of the quotient, we get three decimal places. 

Conversion of Decimals – The overall conversion of fractions into decimals must be initiated with the process of long division where the numerator is represented under the bracket and the denominator is placed outside. Its representation is done with the help of the following image:

Here is a chart of fractions converted into a decimal by using the denominator and converting it into a power of 10:

In this form of conversion, the denominator of the fraction is converted into powers of 10 like 10, 100, 1000, etc.

And so on..

How to convert back decimals into fractions? 

Converting decimals into fractions is consists of a few easy steps:

• The decimal is divided by 1 and then both the denominator and numerator are multiplied by 10 for each number present after the decimal point.

• After multiplying both the numerator and denominator, it should be simplified or reduced into fractions.

Here’s a chart on how decimals are converted into fractions:

0.25 x 100 = 25 

  1    x 100   100

Conversion of decimal into binary.

The conversion from decimal to binary can be done by using many methods.

• One method is to divide the given decimal recursively by 2 until we get zero as the final quotient.

• Then the remainders are written in the reverse order to get the binary value.

One can convert decimal to binary by using this simple method. 

Here is a chart on how one can convert decimal to binary:

By using this chart you can convert decimal to binary. 

Therefore, a decimal system is important to understand the conversions as well as how the numbers are placed before and after the decimal point. The conversion from decimal to binary and decimal to fractions is a very easy technique and can be done by the examples provided above.