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Another Peek Beyond the Point - Decimal Division

Grade 7CBSE

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

🔑Concepts

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Dividing a decimal by 10,100,10, 100, or 10001000: To divide a decimal number by 10,100,10, 100, or 10001000, the digits in the number remain the same, but the decimal point shifts to the left by as many places as there are zeros in the divisor.

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Dividing a decimal by a whole number: Divide the decimal number as though it were a whole number. Place the decimal point in the quotient directly above the decimal point in the dividend.

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Dividing a decimal by another decimal: First, convert the divisor into a whole number by multiplying both the dividend and the divisor by the same power of 1010 (10,100,1000,10, 100, 1000, etc.). Then, proceed with the division as usual.

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Placeholders: If there are not enough digits to the left while shifting the decimal point, add zeros as placeholders.

📐Formulae

Dividend=Divisor×Quotient+Remainder\text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder}

a.b10n=Shift decimal n places to the left\frac{a.b}{10^n} = \text{Shift decimal } n \text{ places to the left}

a.bc.d=a.b×10nc.d×10n (where 10n makes the divisor a whole number)\frac{a.b}{c.d} = \frac{a.b \times 10^n}{c.d \times 10^n} \text{ (where } 10^n \text{ makes the divisor a whole number)}

💡Examples

Problem 1:

Divide 235.4235.4 by 100100.

Solution:

235.4÷100=2.354235.4 \div 100 = 2.354

Explanation:

Since 100100 has two zeros, move the decimal point two places to the left.

Problem 2:

Divide 12.512.5 by 55.

Solution:

2.512.5−10.02.5−2.50\begin{array}{r} 2.5 \\ \hline 12.5 \\ -10.0 \\ \hline 2.5 \\ -2.5 \\ \hline 0 \end{array} Result: 2.52.5

Explanation:

Divide 12.512.5 by 55 just like whole numbers. The decimal point is placed in the quotient right above the decimal point in 12.512.5.

Problem 3:

Divide 0.090.09 by 0.30.3.

Solution:

0.09÷0.3=0.09×100.3×10=0.93=0.30.09 \div 0.3 = \frac{0.09 \times 10}{0.3 \times 10} = \frac{0.9}{3} = 0.3

Explanation:

To make the divisor (0.30.3) a whole number, we multiply both the dividend and divisor by 1010. Then we divide 0.90.9 by 33.

Problem 4:

Find the value of 7.75÷0.257.75 \div 0.25.

Solution:

7.750.25=7.75×1000.25×100=77525=31\frac{7.75}{0.25} = \frac{7.75 \times 100}{0.25 \times 100} = \frac{775}{25} = 31

Explanation:

Multiply both numbers by 100100 to remove the decimals from the divisor. 775÷25=31775 \div 25 = 31.