Addition, Subtraction, Multiplication & Division of Decimals

Addition of decimal numbers

Decimals numbers are added in the same way to how the whole numbers are added. A decimal number has two parts, one is whole number part, another is the decimal part and a decimal point in between whole number and decimal parts.

To add two decimal numbers, their digits are placed one below the other and at their correct places. The digits of whole number part are placed at the ones, tens, hundreds, thousands places and the digits of decimal part are placed at tenths, hundredths, thousandths places.
The addition of decimal numbers always starts from the decimal part and ends at the whole number part. The decimal point in the decimal number obtained after the addition is placed below the other decimals points of given numbers.

Carryovers in addition of decimal numbers are handled same like how they are handles in addition of whole numbers.

Steps to add decimal numbers

Step 1: Place the digits of the whole number part of given decimal numbers at their ones, tens, hundreds, thousands places. Also, place the digits of the decimal part at their tenths, hundredths, thousandths places.
Step 2: Write 0 to fill the places where there are no digits written.
Step 3: Start adding the digits of decimal part first and in the direction from right to left. Keep on adding in the same direction upto the last digit of the whole number part.

Subtraction of decimal numbers

Decimals numbers are subtracted same like how the whole numbers are subtracted.
To subtract two decimal numbers, their digits of whole parts and decimal parts are placed at their correct places. Subtraction also starts from the decimal part and ends at the whole number part.

Steps to subtract decimal numbers

Step 1: First write the largest number and then second number below the first. Write the digits of the whole number part and decimal part at correct places.
Step 2: Write 0 at empty places.
Step 3: Start subtracting the digits from the decimal part and end at whole part.

Multiplication of decimal numbers

Multiplication of decimal numbers with any other numbers generally follows the same steps those are followed to multiply the whole numbers.
The foremost common step for every multiplication is to write the given numbers at their right places without using decimal points. Multiply the numbers same like the whole numbers are multiplied.
After getting an answer, the decimal point is put back to it.
Depending upon what is going to be multiplied with the decimal number, there will be different ways to put back the decimal point in the answer, which are explained as below:

1. Multiply with a whole number
2. Multiply with a decimal number
3. Multiply with 10
4. Multiply with 100
5. Multiply with 1000

1. Multiply with a whole number

In this case, the decimal point is put back in the answer after leaving the number of digits from its right side equal to the number of digits that exist after the decimal point in the given decimal number.

2. Multiply with a decimal number

In the case of multiplying two decimal numbers, the total number of digits after the decimal points of the both given decimal numbers are counted and the decimal point is put back in the answer after leaving the same number of digits from its right side.

3. Multiply with 10

The number 10 has one zero.
To multiply, this one zero is appended after the given decimal number at the end and the decimal point in the answer is shifted from the original position by one position to the right.
One is taken from the number of zeros in 10.

4. Multiply with 100

The number 100 has two zeros.
To multiply, the two zeros ares appended at the end of given decimal number and the decimal point in the answer is shifted from the original position to the right by two positions.
Two is taken from the number of zeros in 100.

5. Multiply with 1000

The number 1000 has three zero.
To multiply, the three zeros are appended at the end of given decimal number and the decimal point in the answer is shifted from the original position by three positions to the right.
Three is taken from the number of zeros in 1000.

Division of decimal numbers

Division of decimal numbers is performed using the long division method. In this method the number to be divided is the dividend, which is used after removing the decimal point. The number which will divide is the divisor. The answer of the division in this method is taken at the end from the quotient.
In dividing the decimal numbers by a number, there are different ways to put back the decimal point in the answer depending upon the number in divisor:

1. Divisor is a whole number
2. Divisor is a decimal number
3. Divisor is 10
4. Divisor is 100
5. Divisor is 1000

1. Divisor is a whole number

If the divisor is whole number, the decimal point is placed after leaving the number of digits from right side of the answer equal to the number of digits after the decimal point in the given decimal number.

2. Divisor is a decimal number

In the case, Subtract the number of digits after the decimal points of divisor from the dividend. Put the decimal point after leaving the same number of digits from the right of the quotient.

In the above example the number of decimal places of dividend are more than the divisor. There can be another case where the number of decimal places of dividend are lesser than the divisor. In such cases the after subtracting the number of decimal points of dividend from the divisor, put as many zeros to the right of the quotient.

3. Divisor is 10

The decimal point is shifted more towards left by one decimal place in the dividend when it is divide by 10. The one place is taken from the one zero in 10.

4. Divisor is 100

In this case, the decimal point is shifted more towards left by two decimal places in the dividend. The two places are taken from the two zeros in 100.

5. Divisor is 1000

In division by 1000, the decimal point is shifted towards left by three decimal places in the dividend again. The three places are taken from the three zeros in 1000.