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Another Peek Beyond the Point - A Quick Recap of Decimals

Grade 7CBSE

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

🔑Concepts

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A decimal number consists of a whole number part and a fractional part separated by a decimal point. For example, in 45.6745.67, 4545 is the whole number part and .67.67 is the decimal part.

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Place Value: To the right of the decimal point, the places are tenths (110\frac{1}{10}), hundredths (1100\frac{1}{100}), thousandths (11000\frac{1}{1000}), and so on.

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Like Decimals: Decimals having the same number of decimal places are called like decimals (e.g., 2.342.34 and 15.9115.91). Unlike decimals can be converted to like decimals by adding zeros at the end (e.g., 0.50.5 becomes 0.500.50).

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Comparison: To compare two decimals, first compare the whole number parts. If they are equal, compare the tenths digits, then hundredths, and so on.

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Addition and Subtraction: To add or subtract decimals, align the decimal points vertically and perform the operation as with whole numbers. Empty places should be filled with 00.

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Multiplication: Multiply the decimals as if they were whole numbers. Count the total number of decimal places in the factors and place the decimal point in the product so that it has the same number of decimal places.

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Division by Powers of 10: When dividing by 10,100,100010, 100, 1000, move the decimal point to the left by as many places as there are zeros in the divisor.

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Division by another Decimal: To divide a decimal by another decimal, multiply both the dividend and divisor by a power of 1010 to make the divisor a whole number, then divide.

📐Formulae

Value=⋯+(d1×10−1)+(d2×10−2)+(d3×10−3)…\text{Value} = \dots + (d_1 \times 10^{-1}) + (d_2 \times 10^{-2}) + (d_3 \times 10^{-3}) \dots

Decimal places in Product=Sum of decimal places in Multiplicands\text{Decimal places in Product} = \text{Sum of decimal places in Multiplicands}

a10n=a×10−n\frac{a}{10^n} = a \times 10^{-n}

a.bcx.y=a.bc×10kx.y×10k (where 10k makes the divisor a whole number)\frac{a.bc}{x.y} = \frac{a.bc \times 10^k}{x.y \times 10^k} \text{ (where } 10^k \text{ makes the divisor a whole number)}

💡Examples

Problem 1:

Add 12.512.5 and 7.857.85.

Solution:

12.50+7.85=20.3512.50 + 7.85 = 20.35

Explanation:

First, convert 12.512.5 to a like decimal 12.5012.50. Align the decimal points and add: 12.50+7.8520.35\begin{array}{r} 12.50 \\ + 7.85 \\ \hline 20.35 \end{array}

Problem 2:

Find the product of 0.4×0.020.4 \times 0.02.

Solution:

0.4×0.02=0.0080.4 \times 0.02 = 0.008

Explanation:

Multiply the whole numbers: 4×2=84 \times 2 = 8. The first number has 11 decimal place and the second has 22 decimal places. The total decimal places in the product must be 1+2=31 + 2 = 3. Therefore, 88 becomes 0.0080.008.

Problem 3:

Divide 0.250.25 by 0.50.5.

Solution:

0.25÷0.5=0.50.25 \div 0.5 = 0.5

Explanation:

To make the divisor 0.50.5 a whole number, multiply both by 1010: 0.25×100.5×10=2.55\frac{0.25 \times 10}{0.5 \times 10} = \frac{2.5}{5} Dividing 2.52.5 by 55 gives 0.50.5.

Problem 4:

Subtract 18.3418.34 from 3030.

Solution:

30.00−18.34=11.6630.00 - 18.34 = 11.66

Explanation:

Convert 3030 to 30.0030.00 to match decimal places. 30.00−18.3411.66\begin{array}{r} 30.00 \\ - 18.34 \\ \hline 11.66 \end{array}