# Powerful Decimals: How to Uncover the Missing Number in Division by Powers of 10

Division by powers of 10 is a cornerstone concept in mathematics, especially when dealing with decimals. The process involves shifting the decimal point, and understanding this can help in determining missing numbers in division equations. Let's explore this concept in depth.

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:

To transform \(3.45\) to \(0.0345\), the decimal point needs to move two places to the left.

**Answer:**

The missing number is \(100\), as \(3.45 \div 100 = 0.0345\).

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!

### Practice Questions:

1. Complete the division sentence: \(4.6 \div \_ = 0.46\).

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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