this 7-digit number is 8,920,000 when rounded to the nearest ten thousand. the digits to the tens and hundreds places are the least and same value. the value of the thousands digit is double that of the ten thousands digit. the sum of all its digits is 24.
8,924,001
This 7 digit number is 8,920,000 when rounded to the nearest ten thousand
7,800,00
8924220
800000
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To solve this problem, we need to analyze the given information step by step.
1. The 7-digit number is 8,920,000 when rounded to the nearest ten thousand.
This tells us that the ten thousands digit is either 8 or 9. Since the number is rounded to 8,920,000, the ten thousands digit cannot be 9.
2. The digits to the tens and hundreds places are the least and have the same value.
Since all the digits in the tens and hundreds places are the least value and equal to each other, we can conclude that both of them must be 0.
3. The value of the thousands digit is double that of the ten thousands digit.
Since the number is rounded to 8,920,000, the thousands digit cannot be 1 as it needs to be double the value of the ten thousands digit. Therefore, the thousands digit must be 2.
4. The sum of all its digits is 24.
Given that the sum of all the digits is 24, we can now calculate the remaining digits by subtracting the known digits from the total sum.
Let's calculate it step by step:
Total sum of all digits = 24
Ten thousands digit = 8 or 9
Tens digit = 0
Hundreds digit = 0
Thousands digit = 2
Remaining sum = Total sum - (Ten thousands digit + Tens digit + Hundreds digit + Thousands digit)
Remaining sum = 24 - (8 + 0 + 0 + 2)
Remaining sum = 14
Now, we need to distribute the remaining sum of 14 among the remaining three digits: the hundreds of thousands, ten thousands, and ones place.
The remaining sum of 14 can be distributed in various combinations. Let's try a few possibilities:
a) Hundreds of thousands = 9, Ten thousands = 6, Ones = 7
(9 + 6 + 0 + 0 + 2 + 0 + 7 = 24)
The 7-digit number would be 9,620,070.
b) Hundreds of thousands = 8, Ten thousands = 5, Ones = 1
(8 + 5 + 0 + 0 + 2 + 0 + 1 = 16)
The 7-digit number would be 8,520,010.
c) Hundreds of thousands = 8, Ten thousands = 6, Ones = 0
(8 + 6 + 0 + 0 + 2 + 0 + 0 = 16)
The 7-digit number would be 8,620,000.
Remember, we are looking for a number that is rounded to 8,920,000 when rounded to the nearest ten thousand. This eliminates option a) and b).
Therefore, the solution to the problem is option c).
So, the 7-digit number that satisfies all the given conditions is 8,620,000.