The difference between the place values of ‘4’ and ‘2’ in the number 833749502 is:
39998
Understanding Place Value Difference
The question asks for the difference between the place values of two specific digits, '4' and '2', in the number 833749502.
First, let's understand what place value means. The place value of a digit in a number depends on its position in the number. Each position corresponds to a power of 10.
Identifying Place Values in 833749502
Let's look at the place value of each digit in the number 833749502:
| Digit | Position | Place Value |
|---|---|---|
| 8 | Hundred Millions | \(8 \times 100,000,000 = 800,000,000\) |
| 3 | Ten Millions | \(3 \times 10,000,000 = 30,000,000\) |
| 3 | Millions | \(3 \times 1,000,000 = 3,000,000\) |
| 7 | Hundred Thousands | \(7 \times 100,000 = 700,000\) |
| 4 | Ten Thousands | \(4 \times 10,000 = 40,000\) |
| 9 | Thousands | \(9 \times 1,000 = 9,000\) |
| 5 | Hundreds | \(5 \times 100 = 500\) |
| 0 | Tens | \(0 \times 10 = 0\) |
| 2 | Units (Ones) | \(2 \times 1 = 2\) |
From the table, we can see:
- The digit '4' is in the Ten Thousands place. Its place value is \(40,000\).
- The digit '2' is in the Units (Ones) place. Its place value is \(2\).
Calculating the Difference
To find the difference between the place values of '4' and '2', we subtract the smaller place value from the larger one:
\text{Difference} = \text{Place value of } '4' - \text{Place value of } '2'
\text{Difference} = 40,000 - 2
Subtracting 2 from 40,000:
\( \begin{array}{@{}c@{\,}c@{}c@{}c@{}c} & 4 & 0 & 0 & 0 & 0 \\ - & & & & & 2 \\ \hline & 3 & 9 & 9 & 9 & 8 \\ \end{array} \)
The difference between the place values of '4' and '2' in 833749502 is \(39,998\).
Revision Table: Key Concepts
| Concept | Description |
|---|---|
| Place Value | The value of a digit determined by its position in a number. |
| Face Value | The actual value of the digit itself, regardless of its position. |
| Difference | The result of subtracting one number from another. |
Additional Information: Expanded Form
Understanding place value is crucial for writing a number in its expanded form. The expanded form of 833749502 is the sum of the place values of all its digits:
\(800,000,000 + 30,000,000 + 3,000,000 + 700,000 + 40,000 + 9,000 + 500 + 0 + 2\)
This also equals 833749502. This shows how each digit contributes to the total value of the number based on its place.
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