Addition of Decimals
We will discuss here about the addition of decimals.
Decimals are added in the same way as we add ordinary numbers. We arrange the
digits in columns and then add as required.
Let us consider some of the following examples on adding decimals.
1. Add 3.4, 4.6 and 5.2
Step I: Write the numbers vertically aligning on the decimal points. Add the tenths. 4 + 6 + 2 = 12 Place 2 in the tenths column and place the point before it.
Carry 1 to the whole number part. Add the whole numbers. 3 + 4 + 5 + 1 = 13 The sum of 3.4, 4.6 and 5.2 is 13.2

The required sum is 13.2

2. Add 14.539, 5 and 3.8
Step I: Write the numbers vertically aligning on the decimal points. Write equivalent decimals of 5 and 3.8 up to three places. 5 = 5.000 3.8
= 3.800 Add thousandths 9 + 0 + 0 = 9. Write 9 under thousandths Add hundredths 3 + 0 + 0 = 3. Write 3 under hundredths Add tenths 5 + 0 + 8 = 13. Write 3 under tenths and carry 1 to ones
place. Add ones. 4 + 5 + 3 + 1 = 13.
Write 3 under ones and carry 1 to tens place. Add tens. 1 + 1 = 2. Write 2
under tens.

The required sum is 23.339

3. Add 46.25, 108.45 and 456.62
We arrange the digits of decimals in columns and then we add
the numbers as usual.
4 6 . 2 5
1 0 8 . 4 5
+ 4 5 6 . 6 2
6 1 1 . 3 2

While adding we ensure that the decimal point of all the
numbers should be in the same column.

Sometimes the numbers to be added may not have digits for each column. In such case, we can add zero at the extreme right or left of a given decimal number.
4. Add 230.45, 189.568 and 25.709
Here we will see adding decimals in two ways. We arrange the digits of decimals in columns and then we add the numbers as usual.
2 3 0 . 4 5
1 8 9 . 5 6 8
+ 2 5 . 7 0 9
4 4 5 . 7 2 7

Or,

2 3 0 . 4 5 0
1 8 9 . 5 6 8
+ 0 2 5 . 7 0 9
4 4 5 . 7 2 7

Questions and Answers on Addition of Decimals:
I. Add the following:
(i) 7.9 + 2.8 + 3.2 + 16.8 = ..............
(ii) 83.1 + 18.2 + 45.4 + 14.7 = ..............
(iii) 24.35 + 19.10 + 28.39 + 5.40 = ..............
(iv) 10.00 + 1.05 + 2.30 + 8.75 = ..............
Answer:
I. (i) 30.70
(ii) 161.40
(iii) 77.24
(iv) 22.10
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Like Decimal Fractions are discussed here. Two or more decimal fractions are called like decimals if they have equal number of decimal places. However the number of digits in the integral part does not matter. 0.43, 10.41, 183.42, 1.81, 0.31 are all like fractions
Decimal numbers can be expressed in expanded form using the placevalue chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is missing either in the integral part or decimal part, substitute with 0.
The rules of multiplying decimals are: (i) Take the two numbers as whole numbers (remove the decimal) and multiply. (ii) In the product, place the decimal point after leaving digits equal to the total number of decimal places in both numbers.
To divide a decimal number by a whole number the division is performed in the same way as in the whole numbers. We first divide the two numbers ignoring the decimal point and then place the decimal point in the quotient in the same position as in the dividend.
To multiply a decimal number by a decimal number, we first multiply the two numbers ignoring the decimal points and then place the decimal point in the product in such a way that decimal places in the product is equal to the sum of the decimal places in the given numbers.
Unlike decimal fractions are discussed here. Two or more decimal fractions are called unlike decimals if they have unequal numbers of decimal places. Let us consider some of the unlike decimals; (i) 8.4, 8.41, 8.412 In 8.4, 8.41, 8.412 the number of decimal places are 1, 2
Equivalent decimal fractions are unlike fractions which are equal in value. Numbers obtained by inserting zeros after the extreme right digit in the decimal part of a decimal number are known as equivalent decimals.
While comparing natural numbers we first compare total number of digits in both the numbers and if they are equal then we compare the digit at the extreme left. If they also equal then we compare the next digit and so on. We follow the same pattern while comparing the
Addition of decimal numbers are similar to addition of whole numbers. We convert them to like decimals and place the numbers vertically one below the other in such a way that the decimal point lies exactly on the vertical line. Add as usual as we learnt in the case of whole
The rules of subtracting decimal numbers are: (i) Write the digits of the given numbers one below the other such that the decimal points are in the same vertical line. (ii) Subtract as we subtract whole numbers. Let us consider some of the examples on subtraction
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