Qn. “Explain the process of decimal multiplication and division. Explain the mathematical justification for moving the decimal point when performing decimal division.”
Response
Decimal multiplication
To multiply decimals, begin by multiplying as though no decimal exists. Then, for each component, count the number of digits after the decimal. Finally, the product should have the same amount of digits as the decimal.
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Explanation by Example
When we multiply by 10 decimals, we raise the figure such that we move the decimal point to the right by ten zeros.
Example: We shift the decimal point to the right once if the decimal number is multiplied by 10.
If we multiply by 100, we shift the decimal point to the right twice.
When we multiply by a thousand, we three times shift the decimal point to the right.
For example, the following product may be calculated:
0.2 x 30
It is helpful to rewrite the decimal number 0.2 in this example to compute the product:
0.1 x 2 = 0.2
The example is as shown below.
0.1 x 2 x 30
This computation has to be carried out since we know how to multiply by one in ten (0,1). We're going to get
6 = 60 x 0.1 = 0.1 x 2 x 30
Likewise, a variety of computations using decimal numbers may be readily performed.
Decimal Division
The process of decimal division involves:
-Adding the same number of places to the right of the decimal point in the dividend.
-In the final quotient, one has to align the decimal point exactly above the decimal point in the dividend.
-Dividing in the same manner as if you were dealing with full numbers.
Mathematical Justification
For the decimal division, we only have to obtain the whole number of the divisor. It is quite simple to deal with one decimal as we would be dividing it by a whole integer. The case shows that the decimal point needs to be moved when performing decimal division. The following steps can help to understand why we move the points:
-Step 1: In dividing 58.5 by 4.5, for example, shift a decimal of the divisor right to create the full number as many times as required. The divisor 45 was so created.
-Step 2: Divide the decimal up to the same number of numbers as you shifted the decimal in the dividend. Thus, 585 is the dividend.
-Step 3: Now, exactly like a normal dividend, divide 485 by 35.
References
http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT_RESOURCE/U03_L2_T2_text_final.html
