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Number - Decimal Operations with Powers of 10 and Whole Numbers

Grade 6IB

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

🔑Concepts

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Multiplying a decimal by a power of 10 (e.g., 10,100,100010, 100, 1000): Move the decimal point to the right by the number of zeros in the power of 10. If there are not enough digits, add zeros as placeholders.

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Dividing a decimal by a power of 10: Move the decimal point to the left by the number of zeros in the power of 10. If there are not enough digits, add zeros to the left of the decimal.

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Multiplying a decimal by a whole number: Ignore the decimal point and multiply the numbers as if they were whole numbers. Then, place the decimal point in the product so that it has the same number of decimal places as the original decimal factor.

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Dividing a decimal by a whole number: Perform long division as you would with whole numbers. Place the decimal point in the quotient directly above the decimal point in the dividend.

📐Formulae

x×10n=Move decimal point n places to the rightx \times 10^{n} = \text{Move decimal point } n \text{ places to the right}

x÷10n=Move decimal point n places to the leftx \div 10^{n} = \text{Move decimal point } n \text{ places to the left}

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

💡Examples

Problem 1:

Calculate 45.678×10045.678 \times 100.

Solution:

45.678×100=4567.845.678 \times 100 = 4567.8

Explanation:

Since 100100 has two zeros, move the decimal point two places to the right. 45.678→456.78→4567.845.678 \rightarrow 456.78 \rightarrow 4567.8.

Problem 2:

Calculate 0.4÷10000.4 \div 1000.

Solution:

0.4÷1000=0.00040.4 \div 1000 = 0.0004

Explanation:

Since 10001000 has three zeros, move the decimal point three places to the left. We add placeholder zeros: 0.4→0.04→0.004→0.00040.4 \rightarrow 0.04 \rightarrow 0.004 \rightarrow 0.0004.

Problem 3:

Find the product of 12.412.4 and 77.

Solution:

12.4×7=86.812.4 \times 7 = 86.8

Explanation:

First, multiply as whole numbers: 124×7124 \times 7.

124×7868\begin{array}{r} 124 \\ \times 7 \\ \hline 868 \end{array}

Since 12.412.4 has one decimal place, the answer must have one decimal place: 86.886.8.

Problem 4:

Divide 15.615.6 by 44.

Solution:

15.6÷4=3.915.6 \div 4 = 3.9

Explanation:

Divide as usual while keeping the decimal point aligned:

3.94)15.6‾−12.03.6−3.60\begin{array}{r} 3.9 \\ 4 \overline{) 15.6} \\ -12 \phantom{.0} \\ \hline 3.6 \\ -3.6 \\ \hline 0 \end{array}