# How to Unravel the Ties: Relationships Between Decimal Place Values

Decimals are fascinating, not just because they represent parts of a whole, but also due to the intricate relationships between their place values. Each position in a decimal number is ten times greater or smaller than its neighboring positions. Let's dive deep into these relationships!

## Relationships Between Decimal Place Values

### Example 1:

Consider the number \(4.32\).

– The digit \(4\) is in the ones place.

– The digit \(3\) is in the tenths place.

– The digit \(2\) is in the hundredths place.

**Here’s the relationship:**

1. The ones place is \(10\) times greater than the tenths place.

2. The tenths place is \(10\) times greater than the hundredths place.

So, \(4\) in the ones place is equivalent to \(40\) in the tenths place. Similarly, \(3\) in the tenths place is equivalent to \(30\) in the hundredths place.

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### Example 2:

Consider the number \(0.567\).

– The digit \(5\) is in the tenths place.

– The digit \(6\) is in the hundredths place.

– The digit \(7\) is in the thousandths place.

**Here’s the relationship:**

1. The tenths place is \(10\) times greater than the hundredths place.

2. The hundredths place is \(10\) times greater than the thousandths place.

So, \(5\) in the tenths place is equivalent to \(50\) in the hundredths place. Similarly, \(6\) in the hundredths place is equivalent to \(60\) in the thousandths place.

Grasping the relationships between decimal place values is essential for understanding the relative value of each position. This knowledge is foundational for various mathematical operations and real-world applications. Keep practicing to solidify your understanding!

### Practice Questions:

1. In the number \(3.14\), how many times greater is the digit in the ones place compared to the tenths place?

2. If you move the digit \(7\) from the tenths place to the hundredths place in the number \(0.7\), what will be its new value?

3. In the number \(0.029\), how many times smaller is the digit in the thousandths place compared to the hundredths place?

4. What is the relationship between the tenths and thousandths place in terms of magnitude?

5. If the digit \(8\) moves from the hundredths place to the tenths place, how many times greater does its value become?

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**Answers:**

1. \(10\) times greater.

2. \(0.07\).

3. \(10\) times smaller.

4. The tenths place is \(100\) times greater than the thousandths place.

5. \(10\) times greater.

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