Alright, let's go through the solution step-by-step.
### Step 1: Arrange the digits to form the largest 7-digit number
Ram has the digits: 8, 4, 0, 2, 6, 5, 3. To determine the largest number possible, we start by arranging the digits in descending order:
[tex]\[ 8, 6, 5, 4, 3, 2, 0 \][/tex]
### Step 2: Adjust positions of specific digits
According to the problem, Ram needs to place the digit 2 at the tens place and the digit 6 at the thousands place.
In a 7-digit number, the positions from left to right are: millions, hundred thousands, ten thousands, thousands, hundreds, tens, units.
So far we have: 8654320 (in descending order)
- Current order: 8 (millions), 6 (hundred thousands), 5 (ten thousands), 4 (thousands), 3 (hundreds), 2 (tens), 0 (units)
But we need to ensure:
- Digit 2 at tens place (6th position from the left)
- Digit 6 at thousands place (4th position from the left)
Firstly, we note that tens place is already occupied by 2, so it remains unchanged.
Next, we need to switch the 4th position (currently 4) with the position where 6 currently is positioned (2nd position, hundred thousands place).
### Step 3: Perform the necessary swaps
1. Swap the 2nd place digit with the 4th place digit:
- Before swap: 8, 6, 5, 4, 3, 2, 0
- After swap: 8, 4, 5, 6, 3, 2, 0
Thus, the adjusted number is:
[tex]\[ 8456320 \][/tex]
### Step 4: Construct the number name in the International Number System
The number 8456320 is read as:
Eight million, four hundred fifty-six thousand, three hundred twenty
### Final Solution to the Given Problem:
(a) The largest 7-digit number formed is:
[tex]\[ 8456320 \][/tex]
(b) The number name in the International Number System is:
Eight million, four hundred fifty-six thousand, three hundred twenty
By following these steps, we can verify Ram's largest 7-digit number and its proper representation in the International Number System.
