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**IMO Class 5 Chapter 4: Multiplication and Division of Decimal Numbers Detailed Notes**

**Decimal Multiplication**

Decimal multiplication is a way of multiplying numbers that have decimal points in them. Consider the decimal-free numbers. Write the result after multiplying the integers as usual. Move the decimal after a certain number of digits, equal to the total number of digits after decimal points, now from the correct position.

Take the example 9.2 x 3.14 into consideration. Start by counting the digits that follow the decimal in both numbers. 9.2 has one digit following the decimal, while 3.14 has two digits. Taking both into account, we obtain 92 and 314 as whole numbers. Add these together to get the answer: 92 x 314 = 28888.

Now take a look at the outcome, starting from the right place the decimal after shifting a total of as many positions as the total of the numbers multiplied. Therefore, there are 1 + 2 = 3 spaces. The result is 28.888 if the decimal is placed three positions to the right of the result. Thus 9.2 × 3.14 = 28.888.

Think over the case 2.66 x 1.004 once more. Determine how many digits there are overall after the decimal. In this instance, 2 + 3= 5 . Multiply both of the decimal-free integers to get the total. So, 266 × 1004= 267064. Place the decimal after 5 positions, starting from the right, to get the answer. So, 2.66 × 1.004 = 2.67064.

**Decimal division**

Students must be familiar with how to arrange decimals for a non-terminating division in order to comprehend the notion of decimal division.

**The Decimal Concept for an Incorrect Division**

Take 8/3 as an example. We are aware that the remaining is 2 when 8 is divided by 3. Additionally, since 2 is less than 3 it cannot be split. After the quotient, we add a decimal to continue the division. After doing so, we can continue to divide the remaining amount by zeroes. Therefore, 8/3 Equals 2.666, where 6 is repeated.

Comparable to decimal multiplication is decimal division. To make the dividend and divisor entire numbers, multiply them by a suitable quotient. As said previously, divide the whole numbers and add the decimal after the quotient.

Think about the case of 26.6/2.4. Here, add 10 to the dividend and the divisor. As a result, the division is 266/24. However, the division retains its original worth. Execute the division, then get the outcome. 266/24 = 11.0833

Think about another example, 20.04/1.8. Here, we can observe that the decimal places in the numerator and denominator differ. We must multiply the numerator by 100 in order to get it to a whole number. Add 100 to the denominator and numerator.

We get 2004/180. Divide right away, then get the outcome.

2004/180 = 11.133

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

**Answer: **Count the total number of digits following decimals in multiplication using BODMAS principles first. The multiplicands are multiplied by two, the decimal is positioned after the second from the right, and the answer is two. 2.6 × 1.3 = 3.38.

We now have 3.38/0.8. Multiplying the numerator and denominator by 100 will make the numerator a full number. The result is 338/80. dividing the total to get the outcome,

338/80 = 4.225

therefore, 2.6 × 1.3 / 0.8 = 4.225

**Also Read:** **How to prepare for Olympiads?**

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