Buzz
Compared to multiplying decimal numbers by natural numbers, the process of multiplying decimal numbers with decimal numbers follows a similar method but is slightly more intricate. It requires careful attention and precision in setting up the operation and calculating the result.
- Learn more: What are Decimal Numbers?
A. Theoretical Section
1. How to Multiply Decimal Numbers with Decimal Numbers?
Every operation follows a set of rules, and multiplying two decimal numbers is no exception. The process involves the following steps:
Step 1: Set up the operation as usual.
Step 2: Perform multiplication as you would with natural numbers.
Step 3: Use the decimal point to separate the digits in the product, aligning them with the corresponding decimal places of the known factors, counting from right to left.
2. Special Case of Multiplying Decimal Numbers
The special case we want to introduce in this multiplication scenario is multiplying a decimal number by numbers like 0.1, 0.01, 0.001, 0.0001, and so on.
* Rule : To multiply a decimal by numbers like 0.1, 0.01, 0.001, 0.0001, and so on, simply shift the decimal point of the decimal number to the left by one, two, three, four,... digits correspondingly.
* Multiplication Technique : Unlike the previous multiplication where we set up and calculate, in this scenario, we just need to apply the rule and mentally calculate to find the accurate answer.
* Note : If the whole part of the given decimal has fewer digits than the number of zeros in 0.1, 0.01, 0.001, and so on, add a zero to the left of the whole part and proceed with the multiplication as usual.
B. Practical Exercise Section
1. Set up and Calculate
a) 4.5 x 2.3
b) 9.11 x 1.2
c) 0.125 x 2.14
d) 2.78 x 5.41
2. Mental Calculation
a) 13.6 x 0.1
b) 213.1 x 0.01
c) 98.2 x 0.001
d) 25.8 x 0.0001
Sample Solution
1. Applying the rule of multiplying decimal numbers, we get:
a) 4.5 x 2.3
4.5
x
2.3
A mysterious journey begins
Embrace the power of 135
Unlock the secrets within
Embark on a numerical dance with 90
10.35
Execution Sequence:
Step 1: Set the equation.
Step 2: Multiply as if multiplying two ordinary natural numbers, from right to left. Multiply 3 by 5 to get 15, write down 5 and carry over 1. Multiply 3 by 4 to get 12, add 1, and get 13. The result of the first multiplication is 135. Multiply 2 by 5 to get 10, write down 0, and carry over 1. Multiply 2 by 4 to get 8, add 1, and get 9. The result of the second multiplication is 90. Align the corresponding columns and add the two results, resulting in 1035.
Multiply 3 by 5 to get 15, write down 5 and carry over 1
Multiply 3 by 4 to get 12, add 1, and get 13
=> The result of the first multiplication is 135
Multiply 2 by 5 to get 10, write down 0, and carry over 1
Multiply 2 by 4 to get 8, add 1, and get 9
=> The result of the second multiplication is 90
Align the corresponding columns and add the two results, resulting in 1035
Step 3 : Count the decimal places in both given factors, totaling 2 digits. Use a comma to separate the two digits in the product, and the final result is 10.35
For questions b), c), d), solve them similarly as above to find the correct answers
2. Apply the rule of multiplying a decimal number by 0, 1; 0.01; 0.001; 0.0001;...
*Answer hint:
a) 1.36
b) 2.131
c) 0.0982
d) 0.00258
We hope that the knowledge shared in this article will assist readers, especially students, in mastering the multiplication of decimal numbers. You can rely on this information to actively review and practice at home, preparing for upcoming lessons with the highest effectiveness.
