 # Addition and Subtraction of Decimals

Decimals in Mathematics are defined as the numbers whose whole part and the fractional part. These two parts are separated by a decimal point. The values on the left of the decimal point represent whole numbers which can be greater than equal to zero. The values on the right of the decimal point are always smaller than one. Decimals are used every day in our daily lives. Weights, money, lengths etc. can be expressed in decimals. Decimals are used in situations which require a higher level of precision level in terms of measurement metrics. Just like whole numbers, we can also carry out simple mathematical operations of addition, subtraction, multiplication, and division with decimals. Further ahead in this article, we will look at the addition and subtraction of decimals in greater detail.

Examples of Decimals:

An example of the decimal is 17.48, where, 17 is the whole number part, and 0.48 is the fractional part.

### Place Value in Decimals

As we move from left to right in decimals, the place value of the digits is divided by 10 subsequently.so, tenth in decimal place value on the right side of the decimal point is 1/10 which is 0.1. Similarly, hundredth is 1/100 or 0.001.

Now, we will look at the rules and solved examples for decimal addition and subtraction one after the other.

Let us look at how to perform the addition of decimal numbers. There are certain rules to be followed while adding decimals. The rules for adding decimals are as follows:

• Firstly, the numbers are padded with zeros. This depends on the maximum number of digits past the decimal point.

• So, if there are two decimal numbers to be added and one number has three digits after the decimal point, and the other number has one digit after the decimal point, we add two zeros to the latter number to make the number of digits after the decimal place equal for both numbers. This is known as padding with zeros.

• This process is known as the conversion of decimals into like decimals.

• After this process, the numbers have to be lined up in a vertical manner so that the place values of both numbers are in sync.

• This means the tenth place digit of one number should be just above or below the tenth-place digit of another number.

• Then, for decimal number addition, it should be done digit wise starting from the rightmost digit and moving towards the left-most digit.

Step 1: Convert decimals into like decimals

Step 2: Line up the numbers as per their place values

Step 3: Perform addition of digits from rightmost digit to left-most digit

Example 1) Add 45.01 and 34.986

Solution) first step is to convert the decimals to like decimals.

We add one zero to 45.01 at the end to make the decimals like.

Next, we will line up the numbers according to the place values and then perform addition.

45.010

+ 34.986

79.996

Example 2) Add 39.999 and 2.9

Solution) first step is to convert the decimals to like decimals.

We add two zeros to 2.9 at the end to make the decimals like.

Next, we will line up the numbers according to the place values and then perform addition.

39.999

+ 02.900

42.899

### Subtraction of decimals

Now, we will learn how to subtract decimals. There are certain rules to be followed while subtracting decimals. The rules for the subtraction of decimals are as follows:

• Firstly, the numbers are padded with zeros. This depends on the maximum number of digits past the decimal point.

• So, if there are two decimal numbers to be added and one number has three digits after the decimal point, and the other number has one digit after the decimal point, we add two zeros to the latter number to make the number of digits after the decimal place equal for both numbers. This is known as padding with zeros.

• This process is known as the conversion of decimals into like decimals.

• After this process, the numbers have to be lined up in a vertical manner so that the place values of both numbers are in sync. The numbers have to line up such that the larger number is on the top of the smaller number.

### Steps to Subtract Decimals

Step 1: Convert decimals into like decimals

Step 2: Line up the numbers as per their place values with a larger number above the smaller number

Step 3: Perform subtraction of digits from rightmost digit to the left-most digit

### Subtraction of Decimals Examples

1. Subtract 3.78 from 10.5

Solution) First step is to make the decimals like, and in the second step then line them up and lastly perform the subtraction.

10.50

- 03.78

6.72

1. what are some real applications where we use addition and subtraction of decimals?

We use several applications in real life which involve addition and subtraction of decimals. It used in scenarios which involve:

Money: bank balances, price tags, cash transfers, discounts etc.

Measurements (capacity, mass, length): the weight of the apples to be purchased, the capacity of the milk carton, length of the door etc.

Temperature: for better precision, we use temperature displays in decimals on our thermometers (degree Celsius, Fahrenheit, Kelvin)

2. why was the concept of decimals introduced?

for example there are four pieces of cake which need to be divided among 5 children. We cannot represent the cake pieces in terms of integers alone as if we equally divide the cake pieces for five children; each child will receive a cake piece whose value will be between 0 and 1. To understand this situation and other similar situations, the concept of decimals was introduced in mathematics. And hence, adding and subtracting decimals is an important topic to learn as it finds it applications in various facets of daily life.