- Analyze the place value of each digit in the number \(5,301,393\).
- Identify that the digit 3 appears in the units place, the hundreds place, and the hundred-thousands place.
- Calculate the contribution of each 3: \(3 \times 1 = 3\), \(3 \times 100 = 300\), and \(3 \times 100,000 = 300,000\).
- Conclude that since each 3 is in a different place value, it holds a different value, making option b the correct choice.
- Final Answer: \(\boxed{b}\)
Explanation
- Understanding Place Value
The number \(5,301,393\) is composed of several digits, each occupying a specific position that determines its contribution to the overall value of the number. This is known as the place-value system. To understand why the digit 3 has different values, we must analyze its position within the number. The positions (from right to left) correspond to powers of 10: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, and millions.
- Analyzing the Digit 3
We break down the number \(5,301,393\) into its individual place values:
- The first '3' from the right is in the ones place: \(3 \times 1 = 3\).
- The digit '9' is in the tens place: \(9 \times 10 = 90\).
- The second '3' from the right is in the hundreds place: \(3 \times 100 = 300\).
- The digit '1' is in the thousands place: \(1 \times 1,000 = 1,000\).
- The digit '0' is in the ten-thousands place: \(0 \times 10,000 = 0\).
- The third '3' from the right is in the hundred-thousands place: \(3 \times 100,000 = 300,000\).
- The digit '5' is in the millions place: \(5 \times 1,000,000 = 5,000,000\).
Each digit's value is the product of the digit and its respective place value. Because the digit 3 occupies three distinct positions (ones, hundreds, and hundred-thousands), it represents three different quantities: 3, 300, and 300,000.
- Concluding the Reasoning and Identifying the Correct Option
By examining the positions of the digit 3, we observe that no two 3s are in the same place value. Each location contributes differently to the total sum, which confirms that the value of a digit is fundamentally tied to its position in the number system. Comparing this to the given options, we find that option 'b' correctly describes this principle: each 3 is in a different place value.
Examples
Place value is essential in everyday life, especially when dealing with money. If you have three \$1 bills, three \$100 bills, and three \$100,000 checks, the digit '3' represents different amounts because of the 'place' each bill or check holds in your total net worth. Understanding this helps you correctly interpret numbers on bank statements, receipts, and even large financial reports.