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Another Peek Beyond the Point - Look Before You Leap!

Grade 7CBSE

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

🔑Concepts

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The decimal point separates the whole number part from the fractional part. Positions to the right of the decimal point are tenths (110\frac{1}{10}), hundredths (1100\frac{1}{100}), and thousandths (11000\frac{1}{1000}).

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To multiply a decimal number by 1010, 100100, or 10001000, shift the decimal point to the right by as many places as there are zeros.

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To multiply two decimal numbers, first multiply them as whole numbers. Then, count the total number of decimal places in both factors and place the decimal point in the product so that it has the same number of decimal places.

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To divide a decimal by 1010, 100100, or 10001000, shift the decimal point to the left by as many places as there are zeros.

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To divide a decimal by another decimal, multiply both the dividend and the divisor by a power of 1010 (like 10,100,100010, 100, 1000) to make the divisor a whole number, then proceed with the division.

📐Formulae

a.bc×10=ab.ca.bc \times 10 = ab.c

a.bc÷10=0.abca.bc \div 10 = 0.abc

Product Decimal Places=Sum of Decimal Places in Factors\text{Product Decimal Places} = \text{Sum of Decimal Places in Factors}

a.bc.d=a.b×10nc.d×10n\frac{a.b}{c.d} = \frac{a.b \times 10^n}{c.d \times 10^n}

💡Examples

Problem 1:

Find the product of 2.52.5 and 0.150.15.

Solution:

Step 1: Multiply as whole numbers: 25×15=37525 \times 15 = 375. Step 2: Count decimal places: 2.52.5 has 11 place and 0.150.15 has 22 places. Total = 1+2=31 + 2 = 3 places. Step 3: Place the point: 0.3750.375.

Explanation:

We ignore the decimal point initially to multiply. The final position of the decimal point is determined by the total number of digits to the right of the decimal points in the original numbers.

Problem 2:

Divide 30.9430.94 by 0.70.7.

Solution:

30.940.7=30.94×100.7×10=309.47\frac{30.94}{0.7} = \frac{30.94 \times 10}{0.7 \times 10} = \frac{309.4}{7} Now divide 309.4309.4 by 77: 309.4÷7=44.2309.4 \div 7 = 44.2

Explanation:

To make the divisor (0.70.7) a whole number, we multiply both the numerator and denominator by 1010. Then we perform standard division.

Problem 3:

Subtract 45.6745.67 from 100.00100.00 using vertical alignment.

Solution:

100.00−45.6754.33\begin{array}{r} 100.00 \\ - 45.67 \\ \hline 54.33 \end{array}

Explanation:

Align the decimal points vertically and subtract as you would with whole numbers, carrying over values where necessary.