Answer

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**Hint:**Even numbers are divisible by 2. From 0-9, 0 is the smallest.

**Complete step by step answer:**

1) We have the following numbers

\[5,{\rm{ 9}},{\rm{ 0}},{\rm{ 2}},{\rm{ }}1\]

Among which, 9 is the largest and 0 is the smallest.

2) To make an even number, our number should be divisible by 2. 0 and 2 are the only numbers divisible by 2.

3) Since, 9>5>2>1>0, our number will have 2 in the last (8th) place and 1 as the first (1st) digit of our number.

\[1\]

4) Now, fill in the largest number next to 0 and go up until all the numbers are used in descending order starting from the 7th digit.

\[10000592\]

5) The nearest 100 is 600 which gives us:

\[10000600\]

**Additional information:**

The question has not asked that the number should be even after rounding it off to nearest 100.

The case is easier if an even number is asked. When we round off any number to the nearest 10s or 100s or 1000s, etc. the end result number is always divisible by 2.

Starting the number from the smallest digit (except 0) ensures that our answer is the smallest possible.

**Note:**

Read the question carefully. Always note down the given and when asked for the greatest number, always choose the greatest among the given numbers as the last digit and smallest as 1st (with the exception of 0).

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