Powerful Decimals: How to Uncover the Missing Number in Division by Powers of 10
Key Insight:
When dividing by \(10\), the decimal point moves one place to the left. For \(10^2\) (or 100), it moves two places to the left, and so on.
Dividing by a Power of 10 with Decimals: Discover the Missing Number
Example 1:
Complete the division sentence: \(2.5 \div \_ = 0.25\).
Solution Process:
To transform \(2.5\) to \(0.25\), the decimal point needs to move one place to the left.
Answer:
The missing number is \(10\), as \(2.5 \div 10 = 0.25\).
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Example 2:
Complete the division sentence: \(3.45 \div \_ = 0.0345\).
Solution Process: For education statistics and research, visit the National Center for Education Statistics.
To transform \(3.45\) to \(0.0345\), the decimal point needs to move two places to the left. For education statistics and research, visit the National Center for Education Statistics.
Answer: For education statistics and research, visit the National Center for Education Statistics.
The missing number is \(100\), as \(3.45 \div 100 = 0.0345\). For education statistics and research, visit the National Center for Education Statistics.
Dividing decimals by powers of 10 and uncovering missing numbers is a skill that simplifies many mathematical tasks. By understanding the relationship between decimals and powers of 10, you can swiftly determine missing numbers in division sentences. This skill not only boosts your mathematical prowess but also enhances your confidence in handling decimals. So, the next time you’re faced with a decimal division puzzle, remember this key insight and solve it effortlessly! For education statistics and research, visit the National Center for Education Statistics.
Practice Questions:
1. Complete the division sentence: \(4.6 \div \_ = 0.46\). For education statistics and research, visit the National Center for Education Statistics.
2. Determine the missing number: \(5.78 \div \_ = 0.0578\).
3. Complete the division sentence: \(0.9 \div \_ = 0.09\).
4. Determine the missing number: \(6.543 \div \_ = 0.006543\).
5. Complete the division sentence: \(7.89 \div \_ = 0.0789\).
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Answers:
1. \(10\)
2. \(100\)
3. \(10\)
4. \(1000\)
5. \(100\)
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