Question 9
Context: Observe the number of digits after the decimal point in the multiplier, the multiplicand and the product. Also note the number of zeroes in the denominator.
Q. By looking at the above examples, can you frame a rule to multiply two decimals?
We will find a pattern in decimal places to form a multiplication rule.
Step 1 — Analyze decimal places in factors
Let us look at the first example. The multiplier 9.5 has one decimal digit. The multiplicand 5 has zero decimal digits. The total decimal digits are .
Let us look at the second example. The multiplier 12.5 has one decimal digit. The multiplicand 7.5 has one decimal digit. The total decimal digits are .
Let us look at the third example. The multiplier 1.64 has two decimal digits. The multiplicand 6 has zero decimal digits. The total decimal digits are .
Let us look at the fourth example. The multiplier 5.7 has one decimal digit. The multiplicand 13.35 has two decimal digits. The total decimal digits are .
Step 2 — Analyze decimal places in products
Now, let us check the product for each example. For 9.5 x 5, the product is 47.5. It has one decimal digit. This matches the total from Step 1.
For 12.5 x 7.5, the product is 93.75. It has two decimal digits. This matches the total from Step 1.
For 1.64 x 6, the product is 9.84. It has two decimal digits. This matches the total from Step 1.
For 5.7 x 13.35, the product is 76.095. It has three decimal digits. This matches the total from Step 1.
Step 3 — Formulate the rule
We observe a clear pattern in all examples. The product's decimal places equal the sum of decimal places. This sum is from the multiplier and multiplicand. Also, denominator zeroes match this sum. This observation helps us frame the rule.
Answer
To multiply two decimals: (i) Multiply the numbers as if they were whole numbers. (ii) Count total decimal places in both original numbers. (iii) Place the decimal point in the product from the right. (iv) The product must have this total number of decimal places.
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