## Decimal number

- A decimal number is a fraction whose denominator is a power of 10. For example, the fraction 4⁄10 can be written in decimal form as 0.4.
- The dot in decimal numbers is called the decimal point.
- The number to the right of the decimal point denotes the numerator of the fraction, that is, the fractional part.
- The number to the left of the decimal point denotes the whole number part of the fraction.
- For example, 4 3⁄10 is expressed as 4.3, where 4 is the whole number part and 0.3 is the fractional part. The decimal point separates the whole number part from the fractional part.

## Decimals in Real Life

In day-to-day life, we need to find the sum or total or find the differences in values. The values of length, weight, money, etc., are not always written in the whole numbers, the values are in decimals also. We use decimal addition and subtraction in everyday life when dealing with:

- Money
- Measurements (length, mass, capacity)
- Temperature

For that, we need to understand how to add and subtract decimals. Decimals can be added or subtracted the same way we add or subtract whole numbers.

## Steps to Add Decimals

**Step 1: Convert decimals to like decimals.**

Decimals that have the same number of digits after the decimal point are called like decimals. 3.42, 2.89, 5.14 are all like decimals because they all have 2 digits after the decimal point.

To make decimals like, we can add zeros on the right of extreme right digits in the decimal part of a number as that does not alter the value.

For example, 3.4 is the same as 3.40, which is also the same as 3.400.

**Step 2:** Write the decimals one below the other as per the places of the digits.

**Step 3: **Add starting from the rightmost digit and moving toward the leftmost digit.

**Step 4: **Place the decimal point under the decimal point in the answer.

## Example of Addition of Decimals

**Let us use the above steps to solve the following.**

**Add 23.45, 13.101, and 345.5 **

**Step 1. Convert to like decimals. **

The maximum digits after the decimal place are 3, so we add zeros in other numbers to get 3 decimal places in all of them.

13.101

23.45 = 23.450

345.5 = 345.500

**Step 2. Line up the decimals.**

2 | 3 | . | 4 | 5 | 0 | |

1 | 3 | . | 1 | 0 | 1 | |

3 | 4 | 5 | . | 5 | 0 | 0 |

**Step 3. Add:**

2 | 3 | . | 4 | 5 | 0 | ||

+ | 1 | 3 | . | 1 | 0 | 1 | |

+ | 3 | 4 | 5 | . | 5 | 0 | 0 |

3 | 8 | 2 | 0 | 5 | 1 |

**Step 4. Place the decimal point in the answer.**

2 | 3 | . | 4 | 5 | 0 | ||

+ | 1 | 3 | . | 1 | 0 | 1 | |

+ | 3 | 4 | 5 | . | 5 | 0 | 0 |

3 | 8 | 2 | . | 0 | 5 | 1 |

**Example: Sienna purchased three laces of length 45 m 50 cm, 23 m 83 cm and 16 m 5 cm. She joined them together to get lace of the greatest length. Find the length of the single string obtained.**

To find the length of a single string, we need to add the lengths of all three laces.

**Write the length of laces as decimal numbers.**

45 m 50 cm = 45.50 m

23 m 83 cm = 23.83 m

16 m 5 cm = 16.05 m

**Convert to like decimals.**

The highest decimal place is 2. All the numbers have 2 decimal places, so they are already like decimals.

**Line up the decimals.**

4 | 5 | . | 5 | 0 | |

2 | 3 | . | 8 | 3 | |

1 | 6 | . | 0 | 5 |

**Add:**

4 | 5 | . | 5 | 0 | |

+ | 2 | 3 | . | 8 | 3 |

+ | 1 | 6 | . | 0 | 5 |

8 | 5 | 3 | 8 |

**Place the decimal in the answer.**

4 | 5 | . | 5 | 0 | |

+ | 2 | 3 | . | 8 | 3 |

+ | 1 | 6 | . | 0 | 5 |

8 | 5 | . | 3 | 8 |

Once you know how to add decimals, subtracting them is quite similar. You must be wondering how is adding and subtracting decimals similar? Let’s look at the steps.

## Steps to Subtract Decimals

**Step 1:** Convert unlike decimals into like decimals.

**Step 2**: Write the digits in their respective columns according to the place.

**Step 3**: Put the decimal point one below the other so that all the decimal points are in the same vertical line.

**Step 4**: Start subtracting from the rightmost digit and move toward the leftmost digit.

**Step 5**: Place the decimal point under the decimal point in the answer.

## Examples of Subtraction of Decimals

**Example 1. Subtract 12.856 from 54.2**

1. **Convert to like decimals**: The highest decimal place is 3, so we add zeros in the other numbers and get 3 decimal places in that too.

12.856 and 54.2 = 54.200

**2**. **Line up the decimals**.

5 | 4 | . | 2 | 0 | 0 | |

1 | 2 | . | 8 | 5 | 6 | |

**3. Subtract the decimals.**

5 | 4 | . | 2 | 0 | 0 | |

− | 1 | 2 | . | 8 | 5 | 6 |

4 | 1 | 3 | 4 | 4 |

**4. Place the decimal point in the answer.**

5 | 4 | . | 2 | 0 | 0 | |

− | 1 | 2 | . | 8 | 5 | 6 |

4 | 1 | . | 3 | 4 | 4 |

**Example 2.** Kylie had 25 m 10 cm of ribbon. She uses 8 m and 13 cm to decorate a skirt. How much ribbon is Kylie left with?

**Solution**:

Length of ribbon Kylie had = 25 m 10 cm = 25.10

Length of ribbon used by Kylie = 8 m 13 cm = 8.13

The remaining length of ribbon = 25.10 – 8.13

= 16.97 m

= 16 m 97 cm

2 | 5 | . | 1 | 0 | |

− | 8 | . | 1 | 3 | |

1 | 6 | . | 9 | 7 |

**Addition and Subtraction of Decimals with Whole numbers**

To add or subtract a decimal with a whole number, change the whole number into a decimal number. A whole number can be changed to a decimal number by placing a decimal point after the whole number and writing the required number of zeros after the decimal point.

For example, the whole number 2 can be written as 2.0 or 2.00 or 2.000 and so on.

Similarly, 6 = 6.0 = 6.00 = 6.000 = 6.000 and so on.

Now follow the steps of addition and subtraction of decimals.

**Example: Add 4 + 5.93 + 7**

**Convert whole numbers to decimals and make all decimals like decimals.**

The highest decimal place is 2, so let’s rewrite all numbers as decimal numbers with 2 decimal places to make them like decimals.

4 = 4.00

5.93

7 = 7.00

**Line up the decimals.**

4 | . | 0 | 0 | |

5 | . | 9 | 3 | |

7 | . | 0 | 0 | |

**Add the decimals.**

4 | . | 0 | 0 | |

+ | 5 | . | 9 | 3 |

+ | 7 | . | 0 | 0 |

1 | 6 | 9 | 3 |

**Place the decimal point in the answer.**

4 | . | 0 | 0 | |

+ | 5 | . | 9 | 3 |

+ | 7 | . | 0 | 0 |

1 | 6 | . | 9 | 3 |

**Example: Subtract 19.523 from 21.**

**Convert a whole number to a decimal number with similar decimal places.**

19.523 has 3 decimal places, so let’s rewrite 21 = 21.000

**Line up the decimals.**

2 | 1 | . | 0 | 0 | 0 | |

1 | 9 | . | 5 | 2 | 3 | |

**Subtract the decimals.**

2 | 1 | . | 0 | 0 | 0 | |

− | 1 | 9 | . | 5 | 2 | 3 |

1 | 4 | 7 | 7 |

**Place the decimal in the answer.**

2 | 1 | . | 0 | 0 | 0 | |

− | 1 | 9 | . | 5 | 2 | 3 |

1 | . | 4 | 7 | 7 |

**In 5th grade adding and subtracting decimals is done. 5th graders must practice adding and subtracting decimals word problems too along with simple decimal problems.**

Fun FactsThe word “decimal” originated in the early seventeenth century from the Latin word “decimus” which means “tenth”.We use decimals when we want precise and accurate answers. |

## Solved Examples

**Example 1: Add 0.56, 12.356, and 152.3**

**Solution:**

The highest decimal place is 3, so let’s change all decimals to like decimals.

0.56 = 0.560

12.356

152.3 = 152.300

Line up the decimals and add and place the decimal in place.

0 | . | 5 | 6 | 0 | |||

+ | 1 | 2 | . | 3 | 5 | 6 | |

+ | 1 | 5 | 2 | . | 3 | 0 | 0 |

1 | 6 | 5 | . | 2 | 1 | 6 |

**Example 2: Solve 920.45 – 222.339**

**Solution:**

The highest decimal place is 3, so let’s change 920.45 to 92.450.

Now let’s line up the decimals and subtract them.

9 | 2 | 0 | . | 4 | 5 | 0 | |

− | 2 | 2 | 2 | . | 3 | 3 | 9 |

6 | 9 | 8 | . | 1 | 1 | 1 |

Now let’s practice adding and subtracting decimals word problems.

**Example 3: Siran bought two articles worth $120.45 and $450.85. She paid $700 to the shopkeeper. How much money will she get back from the shopkeeper?**

**Solution:**

Total cost of article = $120.45 + $450.85 = $571.30

1 | 2 | 0 | . | 4 | 5 | |

+ | 4 | 5 | 0 | . | 8 | 5 |

5 | 7 | 1 | . | 3 | 0 |

Money returned by shopkeeper = $700 – $571.30 = $128.70

7 | 0 | 0 | . | 0 | 0 | |

– | 5 | 7 | 1 | . | 3 | 0 |

1 | 2 | 8 | . | 7 | 0 |

So, Siran will get back $128.70 from the shopkeeper.

## Practice Problems

## Adding and Subtracting Decimals? Definition, Steps, Examples

### 1Which of the following are like decimals?

Like decimals are decimals with the same number of digits after the decimal point.

Both 0.44 and 0.40 have 2 digits after the decimal point, hence they are like decimals.

### 2Which of the following shows the sum of 8 dollar 5 cents and 12 dollar 50 cents?

8 dollar 5 cents = 8.05; 12 dollar 50 cents = 12.50; the sum will be 8.05 + 12.50

### 3The value of 4.5 + 0.999 – 2.86 is equal to

$4.5 + 0.999$ – 2.86 $= (4.500 + 0.999)$ – $2.860$ = $5.499$ – $2.860 = 2.639$

### 4Ryan needs $\$450$ to buy his favourite game. He has 150 dollars and 5 cents left from his pocket money. How much money does he still need?

$\$450.00$ – $\$150.05$ = $\$299.95$

## Frequently Asked Questions

**What is important to remember while adding or subtracting decimals?**

Writing the decimal in columns with the decimal points directly below each other.

**Give examples of real-life applications of adding or subtracting decimals.**

- When dealing with money, weight, distance, capacity, etc., we deal with decimals;
- To calculate the total cost of bills, to calculate the money to be received after payment of bill if you have paid extra to a shopkeeper;
- To find the total weight of things bought.

**Can we multiply and divide two decimals?**

Yes, apart from addition and subtraction, we can perform multiplication and division operations on decimals too.

**Is it compulsory to change the decimals to like decimals for addition and subtraction?**

No, changing decimals to like decimals makes it easier to place the digits and decimal points in columns correctly.