**Product of the face value and place value of 8 in 66,83,405**

The face value of a digit is the actual value of the digit itself, regardless of its position within a number. The place value of a digit, on the other hand, refers to the position of the digit within a number and determines its value.

In the given number 66,83,405, we are asked to find the product of the face value and place value of the digit 8. Let's break it down step by step.

**Step 1: Identify the digit 8**

There are three occurrences of the digit 8 in the number 66,83,405. We need to consider each occurrence separately.

**Step 2: Determine the face value of 8**

The face value of 8 is simply 8, as it is the digit itself. Therefore, the face value of each occurrence of 8 is 8.

**Step 3: Determine the place value of 8**

To determine the place value of 8, we need to consider its position within the number.

- The first occurrence of 8 is in the thousands place, so its place value is 8,000.
- The second occurrence of 8 is in the tens place, so its place value is 80.
- The third occurrence of 8 is in the units place, so its place value is 8.

**Step 4: Calculate the product of face value and place value**

To find the product of the face value and place value of 8, we multiply the face value of 8 with its corresponding place value for each occurrence.

- For the first occurrence, the product is 8 * 8,000 = 64,000.
- For the second occurrence, the product is 8 * 80 = 640.
- For the third occurrence, the product is 8 * 8 = 64.

**Step 5: Sum up the products**

To arrive at the final answer, we add up the products of each occurrence of 8:

64,000 + 640 + 64 = 64,704

Therefore, the product of the face value and place value of 8 in the number 66,83,405 is 64,704.

**Explanation in detail**

The place value of a digit determines its position and value within a number, while the face value represents the actual value of the digit itself. By calculating the product of the face value and place value, we can find the total value contributed by a specific digit in a given number.

In the case of the digit 8 in the number 66,83,405, we identified three occurrences. For each occurrence, we determined the face value as 8 and the corresponding place value based on its position within the number.

By multiplying the face value with the place value for each occurrence and summing up the products, we obtained the final answer of 64,704. This represents the total value contributed by the digit 8 in the number 66,83,405.

It's important to note that the product of the face value and place value provides insight into the significance of a digit within a number. This concept is fundamental in understanding the positional value system and its application in various mathematical operations.

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