Addition and Subtraction In Decimals, Sample Questions

Addition and Subtraction of Decimals is a little trickier than performing the same operations on natural numbers. Integers and whole numbers can't match the precision of decimal numbers, so decimals are used instead of them. It employs a dot in between integers, which is referred to as a decimal point. As a simplified form of fractions, decimals are nothing more than a shortcut. The operations of addition or subtraction of decimals are similar to that of the normal numbers, however, the place values of the digits in the numbers should be rightly matched in the case of Decimals.

Key Terms: Decimals, Addition, Subtraction, Fractions, Whole Numbers, Place Value, Decimal Point, Integers

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What are Decimals?

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Decimals can be defined as the numbers used to express the whole number and fraction together. The whole number is separated from the fraction in decimals by inserting a "." which is called a decimal point. In simpler terms, we can say that they are just another way to represent fractions that allows us to write more precise values like length, weight, distance, money, etc.

For Example, 34.56 is a decimal.

Decimals

Read More: Decimal Expansion of Rational Numbers

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Addition of Decimals

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We're all familiar with the basic operation of the addition of natural numbers. The addition of decimals can be done in a specific way. It takes several steps to add decimals which have been elaborated below.

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How To Add Two Decimals?

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Step 1: The numbers are padded with zeros based on the maximum number of digits following the decimal for each of the integers.

Consider, adding 3.456 to 8.1, the padding is determined by the number of digits following the decimal. Since 3.456 includes three digits following the decimal, we pad it with two zeros after 1. Thus, 8.1 to three decimal places equal 8.100.

Step 2: As may be seen in the given example, the numbers are uniformly dispersed. Arrange the numbers vertically in rows.

8.100

+ 3.456

Step 3: Add the decimal numbers like integers, then position the decimal point properly, as a final step to this process.

   8.100

+ 3.456

= 11.556

Addition of Decimals

Read More: Multiplication and Division of Integers

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Examples For Addition of Decimals

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Example 1: Add 2.081 + 2.34

Solution: Padding with zeroes, the numbers would be 

2.081 

2.340

Lining up the decimals for addition: 

2.081 

+ 2.340

Now, add up the digits as usual 

   2.081 

+ 2.340 

= 4.421

Example 2: Add 0.0075 + 6

Solution: Padding with zeroes, the numbers would be 

0.0075 

6.0000

Lining up the decimals for addition: 

0.0075 

6.0000

Lastly, add up the digits

   0.0075

+ 6.0000

= 6.0075

Read More: Greatest Integer Function

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Subtraction of Decimals

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Subtraction of decimals entails subtracting the decimal number with the smaller whole number component from the decimal number with the larger whole number component. However, some restrictions must be followed when conducting decimal subtraction. The usual rule of carryover is followed as in the normal whole numbers. We arrange the decimal points vertically, add extra zeros to the right, and subtract downward.

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How to Subtract Two Decimals?

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The following steps are used to conduct decimal subtraction:

Step 1: The numbers are padded with zeros based on the maximum number of digits following the decimal for each of the integers.

On subtracting 3.456 from 8.1, the padding is done in accordance with 3.456, as 3.456 has supplementary integers following the decimal. Since 3.456 includes three digits following the decimal, we pad 8.1 to three places as 8.100.

Step 2: As illustrated below, the numerals are vertically aligned with one another. The numbers are stacked in a perpendicular row.

8.100 

- 2.546

Step 3: Lastly, subtract the decimal numbers like integers and insert the decimal point in the proper position.

   8.100 

- 2.546

= 5.554

Let us Subtract 8.7 from 14.5. Here, we split decimals and whole numbers and do subtraction independently. 

14.5 - 8.7 = (14 + 0.5)-(8 + 0.7) = 14 + 0.5 - 8 + 0.7 = (14 − 8) + (0.5 − 0.7) = 6 − 0.2 = 5 + 1.0 − 0.2 = 5 + 0.8 = 5.8

Now, the number 1 is subtracted from 6 to assist with further subtraction. Additionally, the subtraction of 1.0 - 0.2 is identical to the subtraction of 10 - 2 = 8. Additionally, a decimal is assigned to the answer 0.8.

Subtraction of Decimals

Read More: Closure Property

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Examples of Subtraction in Decimals

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Check out the respective illustrations of Decimal Subtraction:

Example 1: Subtraction: 6.402 - 1.24

Solution: Padding with zero: 

6.402

1.240

Now, subtract the digits

 6.402

-1.240

= 5.162

Example 2: Subtraction: 3.2 - 0.83

Solution: Padding with zero: 

3.20

0.83

Now, subtract the numbers 

 3.20

-0.83

=2.37

There are some minor differences between adding decimals and adding whole numbers. Remember that fractions are the base of decimals. When adding fractions, add the fractional parts first, then the whole number parts. If necessary, carry the 1 from the fractional component to the whole number part. When dealing with decimals, it is important to align the decimal points in such a way that both the whole number and the decimal fraction are aligned. Then add each of them.

Read More: Real Numbers

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Things To Remember

• Adding a zero to the end of a decimal number has no effect on its value.
• The answer decimal is the sum of the decimals of all the numbers involved in the addition or subtraction.
• The operations of adding and subtracting with decimals are identical to those performed with whole numbers.
• One of the most crucial things to keep in mind is to stack the decimal points so that they are aligned.
• If the number you're working with has fewer digits after the decimal point than the other one, just put a 0 in the appropriate spot.

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