- The digit \(3\) in \(3,624\) sits in the thousands place, representing \(3,000\).
- The digit \(3\) in \(27,365\) sits in the hundreds place, representing \(300\).
- Dividing \(3,000\) by \(300\) gives \(10\).
- The final answer is \(\boxed{10}\).
Explanation
- Identifying Place Values of the Digit 3
In the number \(3,624\), the digit \(3\) is in the thousands place. Therefore, it represents \(3\) thousands, which is equal to \(3 \times 1,000 = 3,000\). In the number \(27,365\), the digit \(3\) is in the hundreds place. Therefore, it represents \(3\) hundreds, which is equal to \(3 \times 100 = 300\). Our goal is to determine how many times greater \(3,000\) is compared to \(300\).
- Calculating the Multiplier
To find how many times as much the value of the digit \(3\) in \(3,624\) is compared to the value of the digit \(3\) in \(27,365\), we set up the following equation:
\[3,000 = x \times 300\]
To solve for \(x\), we divide both sides by \(300\):
\[x = \frac{3,000}{300}\]
Simplifying the fraction, we get:
\[x = \frac{30}{3} = 10\]
Thus, the digit \(3\) in \(3,624\) represents \(10\) times as much as the value of \(3\) hundreds.
Examples
Understanding place value is essential in everyday life, especially when managing finances. For example, if you have \$3,000 in a savings account versus \$300 in a piggy bank, you can quickly determine that your savings account holds 10 times more money. Recognizing the power of ten associated with each decimal place makes it much easier to compare values, calculate interest, or understand how numbers grow as they shift to higher place value positions.