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Another Peek Beyond the Point - Decimal Multiplication

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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To multiply a decimal number by a whole number, multiply them as if they were whole numbers. Place the decimal point in the product such that it has the same number of decimal places as the original decimal number.

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When multiplying two decimal numbers, multiply them as whole numbers first. The number of decimal places in the final product is the sum of the number of decimal places in the two factors being multiplied. For example, if we multiply a number with 22 decimal places by a number with 11 decimal place, the product will have 2+1=32 + 1 = 3 decimal places.

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Multiplication by Powers of 1010: To multiply a decimal by 10,100, or 100010, 100, \text{ or } 1000, move the decimal point to the right by as many places as there are zeros in the multiplier. If there are fewer digits than required, append zeros to the right.

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The trailing zeros after the last non-zero digit in the decimal part of a product do not change its value. For example, 0.500.50 is the same as 0.50.5.

📐Formulae

Decimal places in Product=Decimal places in Factor 1+Decimal places in Factor 2\text{Decimal places in Product} = \text{Decimal places in Factor 1} + \text{Decimal places in Factor 2}

a.bc×10=ab.ca.bc \times 10 = ab.c

a.bc×100=abca.bc \times 100 = abc

a.bc×1000=abc0a.bc \times 1000 = abc0

💡Examples

Problem 1:

Multiply 2.352.35 by 0.40.4.

Solution:

Step 1: Multiply as whole numbers: 235×4=940235 \times 4 = 940. Step 2: Count decimal places. 2.352.35 has 22 places and 0.40.4 has 11 place. Total places = 2+1=32 + 1 = 3. Step 3: Place the decimal point in 940940 counting 33 places from the right: 0.9400.940. Final Answer: 0.940.94.

Explanation:

We treat the numbers as 235235 and 44 to find the base product, then shift the decimal point according to the sum of decimal places in the factors.

Problem 2:

Calculate 12.05×10012.05 \times 100.

Solution:

12.05×100=120512.05 \times 100 = 1205

Explanation:

Since 100100 has two zeros, the decimal point is shifted two places to the right, moving from before the 00 to after the 55.

Problem 3:

Find the product: 1.2×1.21.2 \times 1.2.

Solution:

First, multiply the whole numbers: 12×1224120144\begin{array}{r} 12 \\ \times 12 \\ \hline 24 \\ 120 \\ \hline 144 \end{array} Both factors have 11 decimal place, so the product must have 1+1=21 + 1 = 2 decimal places. Product: 1.441.44.

Explanation:

Using the vertical multiplication method for 12×1212 \times 12 gives 144144. Applying the rule of sum of decimal places (1+1=21+1=2), the decimal point is placed after the first 11.