Suppose you have visited shopping malls, fuel stations, electricity stations, railway stations, etc. In that case, you may have seen the cost mentioned on your purchase bills. Do you ever notice that there is a dot between the values in the price you pay?

Have you ever wondered what that dot means? How does it differ from the value of the number? In Algebra (the branch of Mathematics), this dot is a Decimal. It plays a significant role in the number system.

In this article, we will read about decimals and their applications.

**What Is Decimal?**

A decimal is a fraction whose denominator is the power of 10, i.e., 10, 100, 1000, and many more. It is denoted by the ‘dot (.)’ between numbers. The dot in a decimal number is called a decimal point, while the digits following the decimal point are smaller than one.

**For example**, the number 345.808 is a decimal number.

Here, 345 is the part of a whole number, and 808 is a fractional or decimal part below that 1 in value.

If we move from left to right places in a decimal number, the decimal place value determines the tenth, hundredth, thousandth, and so on places. Tenth place means 1/10 or 0.1 in decimal form. At the same time, a hundredth place means 1/100 or 0.01 in decimal form.

We can differentiate the decimal values with the help of a place value chart.

Hundred | Tens | Ones | Tenth | Hundredth | Thousandth |

100 | 10 | 1 | 1/10 | 1/100 | 1/1000 |

We can also represent decimal numbers on number lines. On the number line, decimal numbers lie between two continuous integers. We can write decimal numbers both in expanded form and in words.

**For example,**

12.456 can be written as

In expanded form:- 10 + 2 + 410 + 5100 + 61000

In words:- Twelve and four hundred fifty-six thousandth

**Some More Examples Of Decimals**

Here are some examples of decimals that will help you learn more about it.

**Example 1:** Write the following as decimals:

Hundreds (100) | Tens (10) | Ones (1) | Tenth (110) |

5 | 3 | 8 | 1 |

2 | 7 | 3 | 4 |

3 | 5 | 4 | 6 |

**Solution:** The decimal form of the given numbers are:

(i) 538.1

(ii) 273.4

(iii) 354.6

**Example 2:** Write the short form of the following numbers:

(i) 20 + 3 + 510

(ii) 4 + 310 + 7100 + 11000

**Solution: **The short form of the given numbers is as follows:

(i) 23.5

(ii) 4.371

**Arithmetic Operations On Decimals**

Decimal numbers can perform arithmetic operations like addition, subtraction, multiplication, and division like other number systems. Let’s have a look at how to add and subtract decimals.

**Addition Operation On Decimals**

Adding two or more decimal numbers is called adding decimals. However, there are certain rules to follow while you add decimals. Let’s learn more about how to add decimals, the rules to add decimals, and some examples.

**How To Add Decimals?**

A decimal number has a whole number part, a decimal point, and a fractional part. If you want to add decimals, aligning each digit according to their place value one below another is necessary. You can use a place value chart, as described above, to add decimals. The values to the left of the decimal points are called ones, tens, and hundreds, while those to the right side of the decimal point are called tenth, hundredth, thousandth, and so on.

**Rules To Add Decimals**

The following given are some rules that help you with learning how to add decimals:

- Place the digits in decimal numbers according to the place value chart below each other.
- Whenever needed, convert decimal numbers into like decimals.
- You can add zeros to cover up the length of short decimal numbers.
- Add the numbers and the decimal point at its place in the last place.
- In cases where the sum of two tenth place values is more than 9, we will perform the addition similar to additions with carrying numbers.

**Some Examples To Understand How Do You Add Decimals**

Here are some examples that can help you understand how to add decimals in different situations. Let’s have a look.

**Example 1:** Find the sum of 0.29 + 0.36.

**Solution:**

We can place these digits in place value chart as follows:

Ones (1) | Tenth (110) | Hundredth (1100) |

0 | 2 | 9 |

0 | 3 | 6 |

The sum of these digits is given as

0 | 6 | 5 |

Therefore, the sum of 0.29 and 0.36 is 0.65.

**Example 2:** Add decimal numbers 20.62 and 13.02.

**Solution:** Arrange these digits according to their place values below each other.

2 0 . 6 2

+1 3 . 0 2

=3 3 . 6 4

Therefore, the sum of the given decimal numbers is 33.64.

**How To Add Decimals And Whole Numbers?**

Adding decimals and whole numbers is similar to adding two or more decimal numbers. You need to follow a step more before adding a decimal number and a whole number. Add a decimal point to the whole number and then add zeros to make the length of the whole number equal to the decimal number.

Let us take some examples to learn more about how to add decimals with whole numbers.

**Example 1:** Add 3.25, 0.075, and 5.

**Solution:**

Add these numbers, but the place values of each digit below each other, and then add the required number of zeros to the numbers.

3 . 2 5 0

0 . 0 7 5

+ 5 . 0 0 0

= 8 . 3 2 5

Therefore, the sum of given numbers is 8.325.

**Example 2:** What will be the sum of 105 and 1.108?

**Solution:**

To add these numbers, put them according to their place values below each other and add zeros to the required places.

1 0 5 . 0 0 0

+0 0 1 . 1 0 8

=1 0 6 . 1 0 8

Therefore, the sum of the given numbers is 106.108.

**Subtraction Operation On Decimals**

Like the addition operation, subtraction of decimals is done by placing digits according to their place values below each other. After that, you can perform the subtraction operation on the decimal numbers. In cases where you need to borrow numbers, it will similarly operate as in simple subtraction of numbers.

Let us understand how to subtract decimals with the help of some examples.

**Example 1:** Subtract 2.051 km from 5.206.

**Solution:** To subtract the given decimal numbers, put each digit according to their place value below each other.

5 . 2 0 6

– 2 . 0 5 1

=3 . 1 5 5

Therefore, after subtracting the given numbers, we get 3.155 km.

**Example 2:** What is 7.368 – 1.15?

**Solution:** After placing each digit according to their place values below each other,

we get

7 . 3 6 8

-1 . 1 5 0

=6 . 2 1 8

Therefore, 7.368 – 1.15 = 6.218.

**How To Add Decimal In Excel?**

Excel is an excellent tool for calculating various arithmetic operations on numbers. You can add, subtract, multiply, or divide numbers very efficiently with the help of Excel.

To learn how to add decimal numbers in excel, you need to follow the given steps:

**Step 1:** Open the new or existing workbook in Excel.

**Step 2:** Select the column you want to perform the addition operation on decimals.

**Step 3: **Click the right button and select the ‘Format Cells’ option.

**Step 4:** Select the category of your numbers under the ‘Number’ tab.

**Step 5:** Set the decimal place upto 2

**Step 6:** Click on the ‘OK’ option.

In this way, you can add decimal numbers in excel.

**Worksheet On Decimals**

Here are some questions to try to practice decimals and their operations.

Q1. Find the value of:

(i) 11.6 – 9.847

(ii) 27.076 + 0.55 + 0.004

Q2. Naresh walked 5 km 37 m in the morning and 2 km 9 m in the evening. How much distance did he walk in all? (Hint: 1 km = 1000 m)

Q3. Tina had 40 m 5 cm long cloth. She cuts 5 m 70 cm length of cloth from this for making a curtain. How long is the piece of cloth left with her? (Hint: 1 m = 100 cm)

Q4. Ravi purchased 6 kg 500 g rice, 3 kg 10 g sugar, and 20 kg 900g flour. Could you find the total weight of his purchases? (Hint: 1 kg = 1000g)

Q5. Aakash bought vegetables weighing 15 kg. 2 kg 700 g were onions, 4 kg 50 g were tomatoes, and the rest were potatoes. What is the weight of the potatoes?

## Frequently Asked Questions

### 1. How to Add Mixed Numbers?

**Ans. **Multiply the whole number by the sum of the digits.

Add the resulting products together.

If there is a remainder, add it to the next whole number in the problem.

### 2. How to Add Mixed Fractions with Whole Numbers?

**Ans.** Adding mixed fractions is really easy. You just have to follow these steps:

Write down the whole number part of the answer first.

Then, write down the fraction part of the answer and add it to the whole number part.

If there is a remainder, write it down too, and subtract it from 100.

### 3. What are the Steps for Adding Mixed Fractions with the Same Denominators?

**Ans.** To add mixed fractions with the same denominators, you need to reduce each fraction by multiplying the numerator and denominator by the least common multiple of their denominators.For example, if you want to add 1/3 + 1/4, you can do it by multiplying both numbers by 3.

### 4. How to Add Mixed Fractions with Whole Numbers?

**Ans.** Add the whole numbers to get the sum.

For each fraction, find a whole number that goes into both numbers without leaving a remainder (this is called the least common multiple).

Subtract this value from each of the fractions.

Add all of the remaining values together to get your final answer.

### 5. How to Add and Subtract Mixed Fractions?

Ans. To add mixed fractions, you first have to convert them into improper fractions. For example, if you want to add 1/2 + 3/4, you convert the fractions into improper fractions by multiplying them together: (1/2) x (3/4) = 3/8. Then, once you have your improper fraction, you convert it back into a mixed fraction by adding the numerators and the denominators together. To subtract mixed fractions, simply invert the fractional parts of your original numbers: for example, if we wanted to subtract 2/3 from 9/10 and 2/3 = 2 x 3/10 = 6 x 10 = 60% or 0.6 then our final result would be 80%.

#### Related topics

#### Addition and Multiplication Using Counters & Bar-Diagrams

Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]

Read More >>#### Dilation: Definitions, Characteristics, and Similarities

Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]

Read More >>#### How to Write and Interpret Numerical Expressions?

Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]

Read More >>#### System of Linear Inequalities and Equations

Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]

Read More >>
Comments: