**Operations on Decimals**

There are four arithmetic operations: addition, subtraction, multiplication and division.

In this section, you will find the process of adding, subtracting, multiplying and dividing decimal numbers. Let us see each operation one by one.

**Addition and Subtraction of Decimals**

To add or subtract decimals, follow these steps:

1. Convert the given decimals into like decimals.

2. Write the decimals in columns with their decimal points one below the other. For subtraction smaller decimal should be put below the bigger decimal.

3. Perform addition or subtraction in the same way as whole numbers and retain the

decimal point at the same place.

**Example 1:**Find the sum of 417.6, 59.8 and 232.89.

**Solution:**

*Converting the unlike decimals into like decimals, we get 417.60, 59.80 and 232.89.*

417 . 60

59 . 80

+ 232 . 89

------------

710 . 39

------------

Thus, the sum of 417.6, 59.8 and 232.89 is 710.39.

**Example 2:**Subtract 26.42 from 745.55.

**Solution:**

745 . 55

– 26 . 42

-------------

719 . 13

-------------

Thus, the difference between 745.55 and 26.42 is 719.13.

**Multiplication of Decimal Numbers**

**Multiplication of a Decimal by a Whole Number**

To multiply a decimal number with a whole number, ignore the decimal point,

multiply and place the decimal point in the product.

**Example:**Multiply: 6.23 × 7

**Solution:**

*6.23 × 7*

623

× 7

-------

4361

-------

Thus, 6.23 × 7 = 43.61

**Multiplication of Decimal by a Decimal**

To multiply two or more decimals, follow these steps:

1. Ignore the decimal points and multiply the numbers.

2. Place the decimal point in the product so that the number of decimal places in the

product is equal to the sum of the decimal places in the given numbers.

**Example:**Multiply the following: 4.01 × 2.03

**Solution:**5.02 × 2.04

502

× 204

-----------

2008

0000

100400

------------

10.2408

------------

**Multiplication of a Decimal by 10, 100, 1000, etc.**

When we multiply a decimal by 10, 100, 1000, etc. move the decimal point to the right by as many digits as there are zeroes in 10, 100, 1000, ..., etc.

**Example:**

a. 86.47 × 10 = 864.7

b. 23.594 × 100 = 2359.4

c. 27.456 × 1000 = 27456

**Division of Decimal Numbers**

**Division of a Decimal by a Decimal**

To divide a decimal number by a whole number, follow these steps:

1. Change the divisor into a natural number by shifting the decimal point to the right hand side by the same number of places in the divisor as well as dividend.

2. Divide the new dividend by the new divisor (natural number).

3. Put the decimal point in the quotient.

**Example:**Divide: 28.125 by 1.5

**Solution:**28.125 ÷ 1.5 = (28.125 × 10) ÷ (1.5 × 10) = 281.25 ÷ 15

Thus, 281.25 ÷ 15 = 18.75

**Division of a Decimal by 10, 100, 1000, etc.**

While dividing a decimal by 10, 100, 1000, etc., shift the decimal point to the left by as many places as the number of zeroes in the divisor.

**Example:**

a. 56.38 ÷ 10 = 5.638

b. 376.87 ÷ 100 = 3.7687

c. 391.39 ÷ 1000 = 0.39139