A 4-digit number rounded to the nearest ten is 2,470. Rounded to the nearest hundred, it is 2,500. What is the number?

2,469

To find the 4-digit number, we need to consider how rounding works.

When rounding to the nearest ten, we look at the last digit of the number. If the last digit is 0, 1, 2, 3, or 4, we round down to the lower ten. If the last digit is 5, 6, 7, 8, or 9, we round up to the higher ten.

In this case, the number 2,470 is rounded to the nearest ten, so the last digit must be either 0, 1, 2, 3, or 4. Since the number is rounded down to 2,470, we can conclude that the last digit is either 0, 1, 2, 3, or 4.

Next, let's consider rounding to the nearest hundred. When rounding to the nearest hundred, we look at the last two digits of the number. If the last two digits are between 00 and 49, we round down to the lower hundred. If the last two digits are between 50 and 99, we round up to the higher hundred.

In this case, the number 2,470 is rounded to the nearest hundred, so the last two digits must be between 00 and 49. Since the number is rounded up to 2,500, we can conclude that the last two digits are between 00 and 49.

Combining the information from the rounding to the nearest ten and rounding to the nearest hundred, we know that the last two digits are between 00 and 49, and the last digit is between 0 and 4.

By considering all possible combinations of the last two digits (from 00 to 49) and the last digit (from 0 to 4), we can deduce that the only possibility is 2,450.

Therefore, the number is 2,450.