We have studied the concept of decimals and studied the applications of the same with solved examples. We shall now discuss the concept of multiplication of decimals and division of decimals and study the same using solved examples.

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## Multiplication of Decimals

To multiply decimals, count the number of numbers after decimals from the right. Consider the numbers without decimals. Multiply the numbers as normally you will and write the result. Now move from the right place the decimal after so many digits as the total digits after decimal points.

Let us consider the example 9.2 × 3.14. First, count the number of digits after decimal in both the numbers. There is one digit after decimal in 9.2 and 2 digits after decimal in 3.14. Now consider both as whole numbers, we get 92 and 314. Multiply them to obtain the result as 92 × 314 = 28888.

Now considering the result, starting from the right place the decimal after moving a total number of places equal to the sum of numbers in the numbers multiplied. So the number of places is 1 + 2 =3. Place the decimal after 3 places from the right in the result, we get 28.888. Thus 9.2 × 3.14 = 28.888.

Again consider the example 2.66 × 1.004. Count the total number of digits after the decimal. it is 2 + 3= 5 in this case. Consider both the numbers without decimals and multiply them. So, 266 × 1004= 267064. Now moving from the right, place the decimal after 5 positions to obtain the result. So 2.66 × 1.004 = 2.67064

## Division of Decimals

To understand the concept of division of decimals, students need to be aware of how to place decimals for a non-terminating division.

### The Concept of Decimal for an Improper Division

Consider the example of 8/3. We know that when 8 is divided by 3, we get a remainder of 2. And 2 is smaller than 3 and hence cannot be divided. To continue the division we put a decimal after the quotient. This then allows us to further add zeroes to the remainder and continue division. So actually, 8/3 = 2.666 where 6 is recurring.

Division of decimals is similar to the multiplication of decimals. Multiply both the dividend and divisor by a suitable quotient to make them whole numbers. Divide the whole numbers and place the decimal after the quotient as discussed above.

Consider for example 26.6/ 2.4. Here multiply both the dividend and divisor by 10. This makes the division 266/24. However, the value of division does not change. Carry out the division and obtain the result. 266/24 = 11.0833

Now consider another example 20.04/ 1.8. Here, we see that the numerator and denominator have different positions of decimals. To convert the numerator to a whole number we need to multiply it by 100. Multiply both the numerator and denominator by 100. We get 2004/180. Divide now and obtain the result.

2004/180 = 11.133

**Solved Question for You**

**Question 1 :Solve the problem 2.6 × 1.3/ 0.8**

**Answer : **Using BODMAS rules, firstly, counting the total number of digits after decimals in multiplication. It is 2. Converting the multiplicands into whole numbers and multiplying and placing the decimal after 2 positions from the right 2.6 × 1.3 = 3.38.

Now we have 3.38/0.8. To convert the numerator into a whole number multiplying both numerator and denominator by 100. So here we get 338/80. Dividing and obtaining the result,

338/80 = 4.225

thus, 2.6 × 1.3 / 0.8 = 4.225

**Question 2: What are the important rules to keep in mind while multiplying the decimals?**

**Answer:** There is an important rule to remember while multiplying the decimals. The number of decimal places in a product must be equivalent to the sum of the decimal places in the factors.

**Question 3: What are the 4 rules of the decimals?**

**Answer:** We should be proficient in using the 4 basic operations comprising the decimals, these are: Addition, Subtraction, Division, and Multiplication.

**Question 4: What is a decimal value?**

**Answer:** The place value is a positional method of representation where the location of a number with respect to a point determines its value. In the decimal system, the value of the digits depends on the number ‘ten’. A decimal point splits the non-negative powers of ‘10’ (100 = 1, 101 = 10, 102 = 100, 103 = 1000, etc.)

**Question 5: How do we divide a decimal number with another decimal number?**

**Answer:** To divide a decimal number by another decimal number follow the steps given below:

- Shift the decimal point in the divisor to the right side until it becomes a whole number.
- Shift the decimal point in the dividend to the right side through the same number of places as it was shifted to make the divisor a whole number.
- Then, finally divide the new dividend with the new divisor.

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